title: Bremsstrahlung

text: Bremsstrahlung (), from "to brake" and "radiation"; i.e., "braking radiation" or "deceleration radiation", is electromagnetic radiation produced by the deceleration of a charged particle when deflected by another charged particle, typically an electron by an atomic nucleus. The moving particle loses kinetic energy, which is converted into radiation (i.e., photons), thus satisfying the law of conservation of energy. The term is also used to refer to the process of producing the radiation. "Bremsstrahlung" has a continuous spectrum, which becomes more intense and whose peak intensity shifts toward higher frequencies as the change of the energy of the decelerated particles increases.


title: Bremsstrahlung

text: Broadly speaking, "bremsstrahlung" or braking radiation is any radiation produced due to the deceleration (negative acceleration) of a charged particle, which includes synchrotron radiation (i.e., photon emission by a relativistic particle), cyclotron radiation (i.e. photon emission by a non-relativistic particle), and the emission of electrons and positrons during beta decay. However, the term is frequently used in the more narrow sense of radiation from electrons (from whatever source) slowing in matter.


title: Bremsstrahlung

text: Bremsstrahlung emitted from plasma is sometimes referred to as free–free radiation. This refers to the fact that the radiation in this case is created by electrons that are free (i.e., not in an atomic or molecular bound state) before, and remain free after, the emission of a photon. In the same parlance, bound–bound radiation refers to discrete spectral lines (an electron "jumps" between two bound states), while free–bound radiation refers to the radiative combination process, in which a free electron recombines with an ion.


title: Bremsstrahlung

text: If quantum effects are negligible, an accelerating charged particle radiates power as described by the Larmor formula and its relativistic generalization.


title: Bremsstrahlung

text: where formula_2 (the velocity of the particle divided by the speed of light), formula_3 is the Lorentz factor, formula_4 signifies a time derivative of formula_5, and "q" is the charge of the particle.


title: Bremsstrahlung

text: In the case where velocity is parallel to acceleration (i.e., linear motion), the expression reduces to


title: Bremsstrahlung

text: where formula_7 is the acceleration. For the case of acceleration perpendicular to the velocity (formula_8), for example in synchrotrons, the total power is


title: Bremsstrahlung

text: Power radiated in the two limiting cases is proportional to formula_10 formula_11 or formula_12 formula_13. Since formula_14, we see that for particles with the same energy formula_15 the total radiated power goes as formula_16 or formula_17, which accounts for why electrons lose energy to bremsstrahlung radiation much more rapidly than heavier charged particles (e.g., muons, protons, alpha particles). This is the reason a TeV energy electron-positron collider (such as the proposed International Linear Collider) cannot use a circular tunnel (requiring constant acceleration), while a proton-proton collider (such as the Large Hadron Collider) can utilize a circular tunnel. The electrons lose energy due to bremsstrahlung at a rate formula_18 times higher than protons do.


title: Bremsstrahlung

text: where formula_20 is a unit vector pointing from the particle towards the observer, and formula_21 is an infinitesimal bit of solid angle.


title: Bremsstrahlung

text: In the case where velocity is parallel to acceleration (for example, linear motion), this simplifies to


title: Bremsstrahlung

text: The full quantum-mechanical treatment of bremsstrahlung is very involved. The "vacuum case" of the interaction of one electron, one ion, and one photon, using the pure Coulomb potential, has an exact solution that was probably first published by A. Sommerfeld in 1931. This analytical solution involves complicated mathematics, and several numerical calculations have been published, such as by Karzas and Latter. Other approximate formulas have been presented, such as in recent work by Weinberg and Pradler and Semmelrock.


title: Bremsstrahlung

text: This section gives a quantum-mechanical analog of the prior section, but with some simplifications to illustrate the important physics. We give a non-relativistic treatment of the special case of an electron of mass formula_25, charge formula_26, and initial speed formula_27 decelerating in the Coulomb field of a gas of heavy ions of charge formula_28 and number density formula_29. The emitted radiation is a photon of frequency formula_30 and energy formula_31. We wish to find the emissivity formula_32 which is the power emitted per (solid angle in photon velocity space * photon frequency), summed over both transverse photon polarizations. We follow the common astrophysical practice of writing this result in terms of an approximate classical result times the free-free emission Gaunt factor "g" which incorporates quantum and other corrections:


title: Bremsstrahlung

text: formula_34 if formula_35, that is the electron does not have enough kinetic energy to emit the photon. A general, quantum-mechanical formula for formula_36 exists but is very complicated, and usually is found by numerical calculations. We present some approximate results with the following additional assumptions:


title: Bremsstrahlung

text: With these assumptions, two unitless parameters characterize the process: formula_41, which measures the strength of the electron-ion Coulomb interaction, and formula_42, which measures the photon "softness" and we assume is always small (the choice of the factor 2 is for later convenience). In the limit formula_43, the quantum-mechanical Born approximation gives:


title: Bremsstrahlung

text: In the opposite limit formula_45, the full quantum-mechanical result reduces to the purely classical result


title: Bremsstrahlung

text: where formula_47 is the Euler–Mascheroni constant. Note that formula_48 which is a purely classical expression without Planck's constant formula_49.


title: Bremsstrahlung

text: A semi-classical, heuristic way to understand the Gaunt factor is to write it as formula_50 where formula_51 and formula_52 are maximum and minimum "impact parameters" for the electron-ion collision, in the presence of the photon electric field. With our assumptions, formula_53: for larger impact parameters, the sinusoidal oscillation of the photon field provides "phase mixing" that strongly reduces the interaction. formula_52 is the larger of the quantum-mechanical deBroglie wavelength formula_55 and the classical distance of closest approach formula_56 where the electron-ion Coulomb potential energy is comparable to the electron's initial kinetic energy.


title: Bremsstrahlung

text: The above approximations generally apply as long as the argument of the logarithm is large, and break down when it is less than unity. Namely, these forms for the Gaunt factor become negative, which is unphysical. A rough approximation to the full calculations, with the appropriate Born and classical limits, is


title: Bremsstrahlung

text: This section discusses bremsstrahlung emission and the inverse absorption process (called inverse bremsstrahlung) in a macroscopic medium. We start with the equation of radiative transfer, which applies to general processes and not just bremsstrahlung:


title: Bremsstrahlung

text: formula_59 is the radiation spectral intensity, or power per (area * solid angle in photon velocity space * photon frequency) summed over both polarizations. formula_60 is the emissivity, analogous to formula_32defined above, and formula_62 is the absorptivity. formula_60 and formula_62 are properties of the matter, not the radiation, and account for all the particles in the medium - not just a pair of one electron and one ion as in the prior section. If formula_65 is uniform in space and time, then the left-hand side of the transfer equation is zero, and we find


title: Bremsstrahlung

text: If the matter and radiation are also in thermal equilibrium at some temperature, then formula_65must be the blackbody spectrum:


title: Bremsstrahlung

text: Since formula_60 and formula_62 are independent of formula_65, this means that formula_72 must be the blackbody spectrum whenever the matter is in equilibrium at some temperature – regardless of the state of the radiation. This allows us to immediately know both formula_60 and formula_62 once one is known – for matter in equilibrium.


title: Bremsstrahlung

text: NOTE: this section currently gives formulas that apply in the Rayleigh–Jeans limit formula_75, and does not use a quantized (Planck) treatment of radiation. Thus a usual factor like formula_76 does not appear. The appearance of formula_77 in formula_78 below is due to the quantum-mechanical treatment of collisions.


title: Bremsstrahlung

text: In a plasma, the free electrons continually collide with the ions, producing bremsstrahlung. A complete analysis requires accounting for both binary Coulomb collisions as well as collective (dielectric) behavior. A detailed treatment is given by Bekefi, while a simplified one is given by Ichimaru. In this section we follow Bekefi's dielectric treatment, with collisions included approximately via the cutoff wavenumber, formula_79.


title: Bremsstrahlung

text: Consider a uniform plasma, with thermal electrons distributed according to the Maxwell–Boltzmann distribution with the temperature formula_80. Following Bekefi, the power spectral density (power per angular frequency interval per volume, integrated over the whole formula_81 sr of solid angle, and in both polarizations) of the bremsstrahlung radiated, is calculated to be


title: Bremsstrahlung

text: where formula_83 is the electron plasma frequency, formula_84 is the photon frequency, formula_85 is the number density of electrons and ions, and other symbols are physical constants. The second bracketed factor is the index of refraction of a light wave in a plasma, and shows that emission is greatly suppressed for formula_86 (this is the cutoff condition for a light wave in a plasma; in this case the light wave is evanescent). This formula thus only applies for formula_87. This formula should be summed over ion species in a multi-species plasma.


title: Bremsstrahlung

text: The special function formula_88 is defined in the exponential integral article, and the unitless quantity formula_78 is


title: Bremsstrahlung

text: formula_79 is a maximum or cutoff wavenumber, arising due to binary collisions, and can vary with ion species. Roughly, formula_92 when formula_93 (typical in plasmas that are not too cold), where formula_94 eV is the Hartree energy, and formula_95 is the electron thermal de Broglie wavelength. Otherwise, formula_96 where formula_97 is the classical Coulomb distance of closest approach.


title: Bremsstrahlung

text: The formula for formula_100 is approximate, in that it neglects enhanced emission occurring for formula_84 slightly above formula_102.


title: Bremsstrahlung

text: where formula_47 is the Euler–Mascheroni constant. The leading, logarithmic term is frequently used, and resembles the Coulomb logarithm that occurs in other collisional plasma calculations. For formula_107 the log term is negative, and the approximation is clearly inadequate. Bekefi gives corrected expressions for the logarithmic term that match detailed binary-collision calculations.


title: Bremsstrahlung

text: Note the appearance of formula_113 due to the quantum nature of formula_114. In practical units, a commonly used version of this formula for formula_115 is


title: Bremsstrahlung

text: This formula is 1.59 times the one given above, with the difference due to details of binary collisions. Such ambiguity is often expressed by introducing Gaunt factor formula_117, e.g. in one finds


title: Bremsstrahlung

text: For very high temperatures there are relativistic corrections to this formula, that is, additional terms of the order of formula_119


title: Bremsstrahlung

text: If the plasma is optically thin, the bremsstrahlung radiation leaves the plasma, carrying part of the internal plasma energy. This effect is known as the "bremsstrahlung cooling". It is a type of radiative cooling. The energy carried away by bremsstrahlung is called "bremsstrahlung losses" and represents a type of radiative losses. One generally uses the term "bremsstrahlung losses" in the context when the plasma cooling is undesired, as e.g. in fusion plasmas.


title: Bremsstrahlung

text: Polarizational bremsstrahlung (sometimes referred to as "atomic bremsstrahlung") is the radiation emitted by the target's atomic electrons as the target atom is polarized by the Coulomb field of the incident charged particle. Polarizational bremsstrahlung contributions to the total bremsstrahlung spectrum have been observed in experiments involving relatively massive incident particles, resonance processes, and free atoms. However, there is still some debate as to whether or not there are significant polarizational bremsstrahlung contributions in experiments involving fast electrons incident on solid targets.


title: Bremsstrahlung

text: It is worth noting that the term "polarizational" is not meant to imply that the emitted bremsstrahlung is polarized. Also, the angular distribution of polarizational bremsstrahlung is theoretically quite different than ordinary bremsstrahlung.


title: Bremsstrahlung

text: In an X-ray tube, electrons are accelerated in a vacuum by an electric field towards a piece of metal called the "target". X-rays are emitted as the electrons slow down (decelerate) in the metal. The output spectrum consists of a continuous spectrum of X-rays, with additional sharp peaks at certain energies. The continuous spectrum is due to bremsstrahlung, while the sharp peaks are characteristic X-rays associated with the atoms in the target. For this reason, bremsstrahlung in this context is also called continuous X-rays.


title: Bremsstrahlung

text: The formula for Kramers' law is usually given as the distribution of intensity (photon count) formula_120 against the wavelength formula_121 of the emitted radiation:


title: Bremsstrahlung

text: The constant "K" is proportional to the atomic number of the target element, and formula_123 is the minimum wavelength given by the Duane–Hunt law.


title: Bremsstrahlung

text: The spectrum has a sharp cutoff at formula_123, which is due to the limited energy of the incoming electrons. For example, if an electron in the tube is accelerated through 60 kV, then it will acquire a kinetic energy of 60 keV, and when it strikes the target it can create X-rays with energy of at most 60 keV, by conservation of energy. (This upper limit corresponds to the electron coming to a stop by emitting just one X-ray photon. Usually the electron emits many photons, and each has an energy less than 60 keV.) A photon with energy of at most 60 keV has wavelength of at least 21 pm, so the continuous X-ray spectrum has exactly that cutoff, as seen in the graph. More generally the formula for the low-wavelength cutoff, the Duane–Hunt law, is:


title: Bremsstrahlung

text: where "h" is Planck's constant, "c" is the speed of light, "V" is the voltage that the electrons are accelerated through, "e" is the elementary charge, and "pm" is picometres.


title: Bremsstrahlung

text: Beta particle-emitting substances sometimes exhibit a weak radiation with continuous spectrum that is due to bremsstrahlung (see the "outer bremsstrahlung" below). In this context, bremsstrahlung is a type of "secondary radiation", in that it is produced as a result of stopping (or slowing) the primary radiation (beta particles). It is very similar to X-rays produced by bombarding metal targets with electrons in X-ray generators (as above) except that it is produced by high-speed electrons from beta radiation.


title: Bremsstrahlung

text: The "inner" bremsstrahlung (also known as "internal bremsstrahlung") arises from the creation of the electron and its loss of energy (due to the strong electric field in the region of the nucleus undergoing decay) as it leaves the nucleus. Such radiation is a feature of beta decay in nuclei, but it is occasionally (less commonly) seen in the beta decay of free neutrons to protons, where it is created as the beta electron leaves the proton.


title: Bremsstrahlung

text: In electron and positron emission by beta decay the photon's energy comes from the electron-nucleon pair, with the spectrum of the bremsstrahlung decreasing continuously with increasing energy of the beta particle. In electron capture, the energy comes at the expense of the neutrino, and the spectrum is greatest at about one third of the normal neutrino energy, decreasing to zero electromagnetic energy at normal neutrino energy. Note that in the case of electron capture, bremsstrahlung is emitted even though no charged particle is emitted. Instead, the bremsstrahlung radiation may be thought of as being created as the captured electron is accelerated toward being absorbed. Such radiation may be at frequencies that are the same as soft gamma radiation, but it exhibits none of the sharp spectral lines of gamma decay, and thus is not technically gamma radiation.


title: Bremsstrahlung

text: The internal process is to be contrasted with the "outer" bremsstrahlung due to the impingement on the nucleus of electrons coming from the outside (i.e., emitted by another nucleus), as discussed above.


title: Bremsstrahlung

text: In some cases, "e.g." , the bremsstrahlung produced by shielding the beta radiation with the normally used dense materials ("e.g." lead) is itself dangerous; in such cases, shielding must be accomplished with low density materials, "e.g." Plexiglas (Lucite), plastic, wood, or water; as the atomic number is lower for these materials, the intensity of bremsstrahlung is significantly reduced, but a larger thickness of shielding is required to stop the electrons (beta radiation).


title: Bremsstrahlung

text: The dominant luminous component in a cluster of galaxies is the 10 to 10 kelvin intracluster medium. The emission from the intracluster medium is characterized by thermal bremsstrahlung. This radiation is in the energy range of X-rays and can be easily observed with space-based telescopes such as Chandra X-ray Observatory, XMM-Newton, ROSAT, ASCA, EXOSAT, Suzaku, RHESSI and future missions like IXO and Astro-H .


title: Bremsstrahlung

text: In electric discharges, for example as laboratory discharges between two electrodes or as lightning discharges between cloud and ground or within clouds, electrons produce Bremsstrahlung photons while scattering off air molecules. These photons become manifest in terrestrial gamma-ray flashes and are the source for beams of electrons, positrons, neutrons and protons. The appearance of Bremsstrahlung photons also influences the propagation and morphology of discharges in nitrogen-oxygen mixtures with low percentages of oxygen.


title: Bremsstrahlung

text: The complete quantum mechanical description was first performed by Bethe and Heitler. They assumed plane waves for electrons which scatter at the nucleus of an atom, and derived a cross section which relates the complete geometry of that process to the frequency of the emitted photon. The quadruply differential cross section which shows a quantum mechanical symmetry to pair production, is:


title: Bremsstrahlung

text: There formula_127 is the atomic number, formula_128 the fine-structure constant, formula_113 the reduced Planck's constant and formula_130 the speed of light. The kinetic energy formula_131 of the electron in the initial and final state is connected to its total energy formula_132 or its momenta formula_133 via


title: Bremsstrahlung

text: where formula_137 is the photon energy. The directions of the emitted photon and the scattered electron are given by


title: Bremsstrahlung

text: where this relation has to be fulfilled for the velocity formula_143 of the electron in the initial and final state.


title: Bremsstrahlung

text: For practical applications (e.g. in Monte Carlo codes) it can be interesting to focus on the relation between the frequency formula_84 of the emitted photon and the angle between this photon and the incident electron. Köhn and Ebert integrated the quadruply differential cross section by Bethe and Heitler over formula_145 and formula_146 and obtained:


title: Bremsstrahlung

text: An analysis of the doubly differential cross section above shows that electrons whose kinetic energy is larger than the rest energy (511 keV) emit photons in forward direction while electrons with a small energy emit photons isotropically.


title: Bremsstrahlung

text: One mechanism, considered important for small atomic numbers formula_127, is the scattering of a free electron at the shell electrons of an atom or molecule. Since electron–electron bremsstrahlung is a function of formula_127 and the usual electron-nucleus bremsstrahlung is a function of formula_152, electron–electron bremsstrahlung is negligible for metals. For air, however, it plays an important role in the production of terrestrial gamma-ray flashes.


title: Riders of Justice

text: Riders of Justice () is a 2020 Danish action comedy film directed and written by Anders Thomas Jensen. The film was released in Denmark on 19 November 2020, receiving positive reviews from critics.


title: Riders of Justice

text: Mathilde loses her mother in a train accident and her father, Markus, a serving soldier in Afghanistan, comes home to console his grieving daughter. Mathilde and Markus find it difficult to come to terms with the tragedy, causing strain in their relationship. However, Markus is approached by a man named Otto (who was on the same train with Markus's wife) who informs him that the train accident wasn't a coincidence, but a planned murder to eliminate a key witness about to give evidence against the head of Riders of Justice motorbike gang. With the help of Otto's friends, Lennart and Emmenthaler, the group identifies a suspicious man who left the train seconds before the accident as the brother of the Riders of Justice's leader. The group goes to the man's house, intending to interrogate him for information about the accident, but Markus loses control and kills him out of anger. Lennart disposes of the evidence, and encounters a young Ukrainian boy named Bodashka. The Riders interrogate Bodashka for information, leading to their identification of Emmenthaler. The Riders attempt a drive-by shooting on the group, but Markus is able to kill the attackers and rescue Bodashka. Mathilde discovers one of the group's meetings, and Lennart lies and explains that they are actually a therapy group attempting to help Markus with his trauma. As the ensemble prepares another hit on the Riders of Justice, Bodashka explains that the suspicious man was not on the train; Lennart and Otto had convinced Emmenthaler to accept a less accurate facial recognition result, and the suspicious man was actually an Egyptian tourist, meaning that their crusade against the Riders of Justice was committed in error, and the evidence they relied on was a simple coincidence. Markus, learning this, breaks down in anger and frustration, finally lowering his stony facade and crying. The next day, the Riders follow social media connections left by Mathilde's boyfriend and attack the group at Markus' house. Several of them are injured, Mathilde is taken hostage, and Markus is disarmed by the Riders. Otto, Lennart, and Emmenthaler, using weapons training Markus gave them earlier, ambush and kill the Riders, saving Markus and Mathilde. The movie flashes forward to Christmas, where the entire group have joined to celebrate and open presents, and Markus and Mathilde have reconciled.


title: Riders of Justice

text: The movie opened to Danish cinemas on November 19, 2020, selling 150,486 tickets for the opening weekend and pre-premieres; beating out "Another Round" for best selling opening weekend in Denmark that year.


title: Riders of Justice

text: Review aggregator Rotten Tomatoes reports an approval rating of based on reviews, with an average rating of . The website's critics consensus reads: "A darkly humorous revenge thriller with satisfying depth and a dash of savory quirk, "Riders of Justice" makes another compelling case for Mads Mikkelsen as an all-purpose leading man."


title: Riders of Justice

text: The film was met with a favorable critical response from the Danish press. "Politiken" called "Riders of Justice" "Anders Thomas Jensen's best movie since "Flickering Lights"", giving it 5 out of 6 hearts.


title: Riders of Justice

text: "B.T." remarked that the movie does not have as many memorable scenes as a number of Anders Thomas Jensen's previous movies, but it's emotional impact is as has as "Another Round".


title: Nana Komatsu

text: Komatsu was born in Tokyo. She married fellow actor Masaki Suda on November 15, 2021. They had reportedly been dating since March 2020. They co-starred in three films: "Destruction Babies", "Drowning Love" and "Threads - Our Tapestry of Love".


title: Nana Komatsu

text: Komatsu made her film debut in "The World of Kanako" and won numerous Best New Actress awards including the Newcomer of The Year award at the 38th Japan Academy Film Prize. She has been a House Ambassador for Chanel since 2015. She had a contract with Stardust Promotion. In 2016, she played a minor role in Martin Scorsese's film Silence.


title: Nana Komatsu

text: Komatsu was nominated for Outstanding Performance by an Actress in a Supporting Role award at the 43rd Japan Academy Film Prize for her role in the film "Family of Strangers". She starred in the sixth highest grossing Japanese film of 2020, "Threads: Our Tapestry of Love". She was nominated in the Outstanding Performance by an Actress in a Leading Role category at the 44th Japan Academy Film Prize for her role in the film "Threads: Our Tapestry of Love".


title: Nana Komatsu

text: In 2021, Komatsu starred in the films "Moonlight Shadow" and "Parasite in Love". In 2022, she starred with Kentaro Sakaguchi in the film "The Last 10 Years", which had grossed over 2.5 billion yen as of April 11, 2022.


title: Limit of a function

text: In mathematics, the limit of a function is a fundamental concept in calculus and analysis concerning the behavior of that function near a particular input.


title: Limit of a function

text: Formal definitions, first devised in the early 19th century, are given below. Informally, a function "f" assigns an output "f"("x") to every input "x". We say that the function has a limit "L" at an input "p," if "f"("x") gets closer and closer to "L" as "x" moves closer and closer to "p". More specifically, when "f" is applied to any input "sufficiently" close to "p", the output value is forced "arbitrarily" close to "L". On the other hand, if some inputs very close to "p" are taken to outputs that stay a fixed distance apart, then we say the limit "does not exist".


title: Limit of a function

text: The notion of a limit has many applications in modern calculus. In particular, the many definitions of continuity employ the concept of limit: roughly, a function is continuous if all of its limits agree with the values of the function. The concept of limit also appears in the definition of the derivative: in the calculus of one variable, this is the limiting value of the slope of secant lines to the graph of a function.


title: Limit of a function

text: Although implicit in the development of calculus of the 17th and 18th centuries, the modern idea of the limit of a function goes back to Bolzano who, in 1817, introduced the basics of the epsilon-delta technique to define continuous functions. However, his work was not known during his lifetime.


title: Limit of a function

text: In his 1821 book "Cours d'analyse", Cauchy discussed variable quantities, infinitesimals and limits, and defined continuity of formula_1 by saying that an infinitesimal change in "x" necessarily produces an infinitesimal change in "y", while claims that he used a rigorous epsilon-delta definition in proofs. In 1861, Weierstrass first introduced the epsilon-delta definition of limit in the form it is usually written today. He also introduced the notations lim and lim.


title: Limit of a function

text: The modern notation of placing the arrow below the limit symbol is due to Hardy, which is introduced in his book "A Course of Pure Mathematics" in 1908.


title: Limit of a function

text: Imagine a person walking over a landscape represented by the graph of "y" = "f"("x"). Their horizontal position is measured by the value of "x", much like the position given by a map of the land or by a global positioning system. Their altitude is given by the coordinate "y". They walk toward the horizontal position given by "x" = "p". As they get closer and closer to it, they notice that their altitude approaches "L". If asked about the altitude of "x" = "p", they would then answer "L".


title: Limit of a function

text: What, then, does it mean to say, their altitude is approaching "L?" It means that their altitude gets nearer and nearer to "L"—except for a possible small error in accuracy. For example, suppose we set a particular accuracy goal for our traveler: they must get within ten meters of "L". They report back that indeed, they can get within ten vertical meters of "L", since they note that when they are within fifty horizontal meters of "p", their altitude is "always" ten meters or less from "L".


title: Limit of a function

text: The accuracy goal is then changed: can they get within one vertical meter? Yes. If they are anywhere within seven horizontal meters of "p", their altitude will always remain within one meter from the target "L". In summary, to say that the traveler's altitude approaches "L" as their horizontal position approaches "p", is to say that for every target accuracy goal, however small it may be, there is some neighbourhood of "p" whose altitude fulfills that accuracy goal.


title: Limit of a function

text: In fact, this explicit statement is quite close to the formal definition of the limit of a function, with values in a topological space.


title: Limit of a function

text: is to say that "ƒ"("x") can be made as close to "L" as desired, by making "x" close enough, but not equal, to "p".


title: Limit of a function

text: The following definitions, known as ("ε", "δ")-definitions, are the generally accepted definitions for the limit of a function in various contexts.


title: Limit of a function

text: Suppose formula_3 is a function defined on the real line, and there are two real numbers "p" and "L". One would say that the limit of "f", as "x" approaches "p", is "L" and written


title: Limit of a function

text: because for every real "ε" > 0, we can take "δ" = "ε"/4, so that for all real "x", if 0 < |"x" − "p"| < "δ", then |"f"("x") − "L"| < "ε".


title: Limit of a function

text: A more general definition applies for functions defined on subsets of the real line. Let ("a", "b") be an open interval in formula_8, and a number "p" in ("a", "b"). Let formula_9 be a real-valued function defined on "S" — a set contains all of ("a", "b"), except possibly at "p" itself. It is then said that the limit of "f" as "x" approaches "p" is "L," if:


title: Limit of a function

text: because for every real "ε" > 0, we can take "δ" = "ε", so that for all real "x" ≥ −3, if 0 < |"x" − 1| < "δ", then |"f"("x") − 2| < "ε". In this example, "S" = [−3, ∞) contains open intervals around the point 1 (for example, the interval (0, 2)).


title: Limit of a function

text: Here, note that the value of the limit does not depend on "f" being defined at "p", nor on the value "f"("p")—if it is defined. For example,


title: Limit of a function

text: because for every "ε" > 0, we can take "δ" = "ε"/2, so that for all real "x" ≠ 1, if 0 < |"x" − 1| < "δ", then |"f"("x") − 3| < "ε". Note that here "f"(1) is undefined.


title: Limit of a function

text: The letters "ε" and "δ" can be understood as "error" and "distance". In fact, Cauchy used "ε" as an abbreviation for "error" in some of his work, though in his definition of continuity, he used an infinitesimal formula_13 rather than either "ε" or "δ" (see "Cours d'Analyse"). In these terms, the error ("ε") in the measurement of the value at the limit can be made as small as desired, by reducing the distance ("δ") to the limit point. As discussed below, this definition also works for functions in a more general context. The idea that "δ" and "ε" represent distances helps suggest these generalizations.


title: Limit of a function

text: Alternatively, "x" may approach "p" from above (right) or below (left), in which case the limits may be written as


title: Limit of a function

text: respectively. If these limits exist at p and are equal there, then this can be referred to as "the" limit of "f"("x") at "p". If the one-sided limits exist at "p", but are unequal, then there is no limit at "p" (i.e., the limit at "p" does not exist). If either one-sided limit does not exist at "p", then the limit at "p" also does not exist.


title: Limit of a function

text: Apart from open intervals, limits can be defined for functions on arbitrary subsets of R, as follows : let formula_18 be a real-valued function defined on arbitrary formula_19. Let "p" be a limit point of "S"—that is, "p" is the limit of some sequence of elements of "S" distinct from p. Then we say the limit of "f", as "x" approaches "p" from values in "S", is "L", written


title: Limit of a function

text: The condition that "f" be defined on "S" is that "S" be a subset of the domain of "f". This generalization includes as special cases limits on an interval, as well as left-handed limits of real-valued functions (e.g., by taking "S" to be an open interval of the form formula_22), and right-handed limits (e.g., by taking "S" to be an open interval of the form formula_23). It also extends the notion of one-sided limits to the included endpoints of (half-)closed intervals, so the square root function "f"("x") = can have limit 0 as x approaches 0 from above:


title: Limit of a function

text: since for every "ε" > 0, we may take "δ" = "ε" such that for all "x" ≥ 0, if 0 < |"x" − 0| < "δ", then |"f"("x") − 0| < "ε".


title: Limit of a function

text: The definition of limit given here does not depend on how (or whether) "f" is defined at "p". refers to this as a "deleted limit", because it excludes the value of "f" at "p". The corresponding non-deleted limit does depend on the value of "f" at "p", if "p" is in the domain of "f". Let formula_18 be a real-valued function. The non-deleted limit of "f", as "x" approaches "p", is "L" if


title: Limit of a function

text: The definition is the same, except that the neighborhood now includes the point "p", in contrast to the deleted neighborhood . This makes the definition of a non-deleted limit less general. One of the advantages of working with non-deleted limits is that they allow to state the theorem about limits of compositions without any constraints on the functions (other than the existence of their non-deleted limits) ().


title: Limit of a function

text: has no limit at formula_28 (the left-hand limit does not exist due to the oscillatory nature of the sine function, and the right-hand limit does not exist due to the asymptotic behaviour of the reciprocal function), but has a limit at every other "x"-coordinate.


title: Limit of a function

text: has a limit at every non-zero "x"-coordinate (the limit equals 1 for negative "x" and equals 2 for positive "x"). The limit at "x" = 0 does not exist (the left-hand limit equals 1, whereas the right-hand limit equals 2).


title: Limit of a function

text: Let formula_35 be a function defined on formula_36. The limit of "f" as "x" approaches infinity is "L", denoted


title: Limit of a function

text: because for every "ε" > 0, we can take "c" = 3/"ε" such that for all real "x", if "x" > "c", then |"f"("x") − 4| < "ε".


title: Limit of a function

text: because for every "ε" > 0, we can take "c" = max{1, −ln("ε")} such that for all real "x", if "x" < −"c", then |"f"("x") − 0| < "ε".


title: Limit of a function

text: For a function whose values grow without bound, the function diverges and the usual limit does not exist. However, in this case one may introduce limits with infinite values.


title: Limit of a function

text: Let formula_35 be a function defined on formula_36. The statement the limit of "f" as "x" approaches "p" is infinity, denoted


title: Limit of a function

text: because for every "N" > 0, we can take "δ" = 1/ such that for all real "x" > 0, if 0 < "x" − 1 < "δ", then "f"("x") > "N".


title: Limit of a function

text: These ideas can be combined in a natural way to produce definitions for different combinations, such as


title: Limit of a function

text: because for every "N" > 0, we can take "δ" = "e" such that for all real "x" > 0, if 0 < "x" − 0 < "δ", then "f"("x") < −"N".


title: Limit of a function

text: These notions of a limit attempt to provide a metric space interpretation to limits at infinity. In fact, they are consistent with the topological space definition of limit if


title: Limit of a function

text: In this case, R is a topological space and any function of the form "f": "X" → "Y" with "X", "Y"⊆ R is subject to the topological definition of a limit. Note that with this topological definition, it is easy to define infinite limits at finite points, which have not been defined above in the metric sense.


title: Limit of a function

text: Many authors allow for the projectively extended real line to be used as a way to include infinite values as well as extended real line. With this notation, the extended real line is given as and the projectively extended real line is R ∪ {∞} where a neighborhood of ∞ is a set of the form The advantage is that one only needs three definitions for limits (left, right, and central) to cover all the cases.


title: Limit of a function

text: As presented above, for a completely rigorous account, we would need to consider 15 separate cases for each combination of infinities (five directions: −∞, left, central, right, and +∞; three bounds: −∞, finite, or +∞). There are also noteworthy pitfalls. For example, when working with the extended real line, formula_53 does not possess a central limit (which is normal):


title: Limit of a function

text: In contrast, when working with the projective real line, infinities (much like 0) are unsigned, so, the central limit "does" exist in that context:


title: Limit of a function

text: In certain applications of numerical differentiation and integration, it is, for example, convenient to have signed zeroes.


title: Limit of a function

text: A simple reason has to do with the converse of formula_56, namely, it is convenient for formula_57 to be considered true.


title: Limit of a function

text: There are three basic rules for evaluating limits at infinity for a rational function "f"("x") = "p"("x")/"q"("x"): (where "p" and "q" are polynomials):


title: Limit of a function

text: If the limit at infinity exists, it represents a horizontal asymptote at "y" = "L". Polynomials do not have horizontal asymptotes; such asymptotes may however occur with rational functions.


title: Limit of a function

text: By noting that |"x" − "p"| represents a distance, the definition of a limit can be extended to functions of more than one variable. In the case of a function formula_58 defined on formula_59, we defined the limit as follows: the limit of "f" as ("x", "y") approaches ("p", "q") is "L", written


title: Limit of a function

text: Here is the Euclidean distance between ("x", "y") and ("p", "q"). (This can in fact be replaced by any norm ||("x", "y") − ("p", "q")||, and be extended to any number of variables.)


title: Limit of a function

text: because for every "ε" > 0, we can take "δ" = such that for all real "x" ≠ 0 and real "y" ≠ 0, if 0 < < "δ", then |"f"("x", "y") − 0| < "ε".


title: Limit of a function

text: Similar to the case in single variable, the value of "f" at ("p", "q") does not matter in this definition of limit.


title: Limit of a function

text: For such a multivariable limit to exist, this definition requires the value of "f" approaches "L" along every possible path approaching ("p", "q"). In the above example, the function


title: Limit of a function

text: satisfies this condition. This can be seen by considering the polar coordinates ("x", "y") = ("r" cos("θ"), "r" sin("θ")) → (0, 0), which gives


title: Limit of a function

text: Here "θ" = "θ"("r") is a function of "r" which controls the shape of the path along which "f" is approaching ("p", "q"). Since cos("θ") is bounded between [−1, 1], by the sandwich theorem, this limit tends to 0.


title: Limit of a function

text: Since the two values do not agree, "f" does not tend to a single value as ("x", "y") approaches (0, 0).


title: Limit of a function

text: Although less commonly used, there is another type of limit for a multivariable function, known as the multiple limit. For a two-variable function, this is the double limit. Let formula_58 be defined on formula_59, we say the double limit of "f" as "x" approaches "p" and "y" approaches "q" is "L", written


title: Limit of a function

text: For such a double limit to exist, this definition requires the value of "f" approaches "L" along every possible path approaching ("p", "q"), excluding the two lines "x" = "p" and "y" = "q". As a result, the multiple limit is a weaker notion than the ordinary limit: if the ordinary limit exists and equals "L", then the multiple limit exists and also equals "L". Note that the converse is not true: the existence of the multiple limits does not imply the existence of the ordinary limit. Consider the example


title: Limit of a function

text: The concept of multiple limit can extend to the limit at infinity, in a way similar to that of a single variable function. For formula_58, we say the double limit of "f" as "x" and "y" approaches infinity is "L", written


title: Limit of a function

text: Let formula_58. Instead of taking limit as ("x", "y") → ("p", "q"), we may consider taking the limit of just one variable, say, "x" → "p", to obtain a single-variable function of "y", namely formula_82. In fact, this limiting process can be done in two distinct ways. The first one is called pointwise limit. We say the pointwise limit of "f" as "x" approaches "p" is "g", denoted


title: Limit of a function

text: Here, "δ" = "δ"("ε", "y") is a function of both "ε" and "y". Each "δ" is chosen for a "specific point" of "y". Hence we say the limit is pointwise in "y". For example,


title: Limit of a function

text: because for every fixed "y", the limit is clearly 0. Note that this argument fails if "y" is not fixed: if "y" is very close to "π"/2, the value of the fraction may deviate from 0.


title: Limit of a function

text: This leads to another definition of limit, namely the uniform limit. We say the uniform limit of "f" on "T" as "x" approaches "p" is "g", denoted


title: Limit of a function

text: Here, "δ" = "δ"("ε") is a function of only "ε" but not "y". In other words, "δ" is "uniformly applicable" to all "y" in "T". Hence we say the limit is uniform in "y". For example,


title: Limit of a function

text: because for all real "y", cos("y") is bounded between [−1, 1]. Hence no matter how "y" behaves, we may use the sandwich theorem to show that the limit is 0.


title: Limit of a function

text: Let formula_58. We may consider taking the limit of just one variable, say, "x" → "p", to obtain a single-variable function of "y", namely formula_82, and then take limit in the other variable, namely "y" → "q", to get a number formula_99. Symbolically,


title: Limit of a function

text: This limit is known as iterated limit of the multivariable function. Note that the order of taking limits may affect the result, i.e.,


title: Limit of a function

text: A sufficient condition of equality is given by the Moore-Osgood theorem, which requires the limit formula_102 to be uniform on "T".


title: Limit of a function

text: Suppose "M" and "N" are subsets of metric spaces "A" and "B", respectively, and "f" : "M" → "N" is defined between "M" and "N", with "x" ∈ "M," "p" a limit point of "M" and "L" ∈ "N". It is said that the limit of "f" as "x" approaches "p" is "L" and write


title: Limit of a function

text: Again, note that "p" need not be in the domain of "f", nor does "L" need to be in the range of "f", and even if "f"("p") is defined it need not be equal to "L".


title: Limit of a function

text: The limit in Euclidean space is a direct generalization of limits to vector-valued functions. For example, we may consider a function formula_105 such that


title: Limit of a function

text: In this example, the function concerned are finite-dimension vector-valued function. In this case, the limit theorem for vector-valued function states that if the limit of each component exists, then the limit of a vector-valued function equals the vector with each component taken the limit:


title: Limit of a function

text: One might also want to consider spaces other than Euclidean space. An example would be the Manhattan space. Consider formula_110 such that


title: Limit of a function

text: Since this is also a finite-dimension vector-valued function, the limit theorem stated above also applies.


title: Limit of a function

text: Finally, we will discuss the limit in function space, which has infinite dimensions. Consider a function "f"("x", "y") in the function space formula_114. We want to find out as "x" approaches "p", how "f"("x", "y") will tend to another function "g"("y"), which is in the function space formula_115. The "closeness" in this function space may be measured under the uniform metric. Then, we will say the uniform limit of "f" on "T" as "x" approaches "p" is "g" and write


title: Limit of a function

text: In fact, one can see that this definition is equivalent to that of the uniform limit of a multivariable function introduced in the previous section.


title: Limit of a function

text: Suppose "X","Y" are topological spaces with "Y" a Hausdorff space. Let "p" be a limit point of Ω ⊆ "X", and "L" ∈"Y". For a function "f" : Ω → "Y", it is said that the limit of "f" as "x" approaches "p" is "L", written


title: Limit of a function

text: This last part of the definition can also be phrased "there exists an open punctured neighbourhood "U" of "p" such that "f"("U"∩Ω) ⊆ "V" ".


title: Limit of a function

text: Note that the domain of "f" does not need to contain "p". If it does, then the value of "f" at "p" is irrelevant to the definition of the limit. In particular, if the domain of "f" is "X" − {"p"} (or all of "X"), then the limit of "f" as "x" → "p" exists and is equal to "L" if, for all subsets Ω of "X" with limit point "p", the limit of the restriction of "f" to Ω exists and is equal to "L". Sometimes this criterion is used to establish the "non-existence" of the two-sided limit of a function on R by showing that the one-sided limits either fail to exist or do not agree. Such a view is fundamental in the field of general topology, where limits and continuity at a point are defined in terms of special families of subsets, called filters, or generalized sequences known as nets.


title: Limit of a function

text: Alternatively, the requirement that "Y" be a Hausdorff space can be relaxed to the assumption that "Y" be a general topological space, but then the limit of a function may not be unique. In particular, one can no longer talk about "the limit" of a function at a point, but rather "a limit" or "the set of limits" at a point.


title: Limit of a function

text: A function is continuous at a limit point "p" of and in its domain if and only if "f"("p") is "the" (or, in the general case, "a") limit of "f"("x") as "x" tends to "p".


title: Limit of a function

text: There is another type of limit of a function, namely the sequential limit. Let be a mapping from a topological space "X" into a Hausdorff space "Y", a limit point of "X" and . The sequential limit of "f" as "x" tends to "p" is "L" if


title: Limit of a function

text: If "L" is the limit (in the sense above) of "f" as "x" approaches "p", then it is a sequential limit as well, however the converse need not hold in general. If in addition "X" is metrizable, then "L" is the sequential limit of "f" as "x" approaches "p" if and only if it is the limit (in the sense above) of "f" as "x" approaches "p".


title: Limit of a function

text: For functions on the real line, one way to define the limit of a function is in terms of the limit of sequences. (This definition is usually attributed to Eduard Heine.) In this setting:


title: Limit of a function

text: if, and only if, for all sequences formula_121 (with formula_121 not equal to "a" for all "n") converging to formula_123 the sequence formula_124 converges to formula_99. It was shown by Sierpiński in 1916 that proving the equivalence of this definition and the definition above, requires and is equivalent to a weak form of the axiom of choice. Note that defining what it means for a sequence formula_121 to converge to formula_123 requires the epsilon, delta method.


title: Limit of a function

text: Similarly as it was the case of Weierstrass's definition, a more general Heine definition applies to functions defined on subsets of the real line. Let "f" be a real-valued function with the domain "Dm"("f"). Let "a" be the limit of a sequence of elements of "Dm"("f") \ {"a"}. Then the limit (in this sense) of "f" is "L" as "x" approaches "p"


title: Limit of a function

text: if for every sequence formula_121 ∈ "Dm"("f") \ {"a"} (so that for all "n", formula_121 is not equal to "a") that converges to "a", the sequence formula_124 converges to formula_99. This is the same as the definition of a sequential limit in the preceding section obtained by regarding the subset "Dm"("f") of R as a metric space with the induced metric.


title: Limit of a function

text: if and only if for all formula_133, formula_134 is infinitesimal whenever formula_135 is infinitesimal. Here formula_136 are the hyperreal numbers and formula_137 is the natural extension of "f" to the non-standard real numbers. Keisler proved that such a hyperreal definition of limit reduces the quantifier complexity by two quantifiers. On the other hand, Hrbacek writes that for the definitions to be valid for all hyperreal numbers they must implicitly be grounded in the ε-δ method, and claims that, from the pedagogical point of view, the hope that non-standard calculus could be done without ε-δ methods cannot be realized in full.


title: Limit of a function

text: Bŀaszczyk et al. detail the usefulness of microcontinuity in developing a transparent definition of uniform continuity, and characterize Hrbacek's criticism as a "dubious lament".


title: Limit of a function

text: At the 1908 international congress of mathematics F. Riesz introduced an alternate way defining limits and continuity in concept called "nearness". A point formula_138 is defined to be near a set formula_139 if for every formula_140 there is a point formula_141 so that formula_142. In this setting the


title: Limit of a function

text: if and only if for all formula_139, formula_99 is near formula_146 whenever formula_123 is near formula_148.


title: Limit of a function

text: Here formula_146 is the set formula_150. This definition can also be extended to metric and topological spaces.


title: Limit of a function

text: The notion of the limit of a function is very closely related to the concept of continuity. A function "ƒ" is said to be continuous at "c" if it is both defined at "c" and its value at "c" equals the limit of "f" as "x" approaches "c":


title: Limit of a function

text: If a function "f" is real-valued, then the limit of "f" at "p" is "L" if and only if both the right-handed limit and left-handed limit of "f" at "p" exist and are equal to "L".


title: Limit of a function

text: The function "f" is continuous at "p" if and only if the limit of "f"("x") as "x" approaches "p" exists and is equal to "f"("p"). If "f" : "M" → "N" is a function between metric spaces "M" and "N", then it is equivalent that "f" transforms every sequence in "M" which converges towards "p" into a sequence in "N" which converges towards "f"("p").


title: Limit of a function

text: If "N" is a normed vector space, then the limit operation is linear in the following sense: if the limit of "f"("x") as "x" approaches "p" is "L" and the limit of "g"("x") as "x" approaches "p" is "P", then the limit of "f"("x") + g("x") as "x" approaches "p" is "L" + "P". If "a" is a scalar from the base field, then the limit of "af"("x") as "x" approaches "p" is "aL".


title: Limit of a function

text: If "f" and "g" are real-valued (or complex-valued) functions, then taking the limit of an operation on "f"("x") and "g"("x") (e.g., formula_152"," formula_153"," formula_154"," formula_155"," formula_156) under certain conditions is compatible with the operation of limits of "f(x)" and "g(x)". This fact is often called the algebraic limit theorem. The main condition needed to apply the following rules is that the limits on the right-hand sides of the equations exist (in other words, these limits are finite values including 0). Additionally, the identity for division requires that the denominator on the right-hand side is non-zero (division by 0 is not defined), and the identity for exponentiation requires that the base is positive, or zero while the exponent is positive (finite).


title: Limit of a function

text: These rules are also valid for one-sided limits, including when "p" is ∞ or −∞. In each rule above, when one of the limits on the right is ∞ or −∞, the limit on the left may sometimes still be determined by the following rules.


title: Limit of a function

text: In other cases the limit on the left may still exist, although the right-hand side, called an "indeterminate form", does not allow one to determine the result. This depends on the functions "f" and "g". These indeterminate forms are:


title: Limit of a function

text: it does "not" follow that formula_160. However, this "chain rule" does hold if one of the following "additional" conditions holds:


title: Limit of a function

text: As an example of this phenomenon, consider the following function that violates both additional restrictions:


title: Limit of a function

text: Thus, the naïve chain rule would suggest that the limit of "f"("f"("x")) is 0. However, it is the case that


title: Limit of a function

text: This can be proven by dividing both the numerator and denominator by formula_174. If the numerator is a polynomial of higher degree, the limit does not exist. If the denominator is of higher degree, the limit is 0.


title: Limit of a function

text: This rule uses derivatives to find limits of indeterminate forms or , and only applies to such cases. Other indeterminate forms may be manipulated into this form. Given two functions and , defined over an open interval containing the desired limit point "c", then if:


title: Limit of a function

text: Specifying an infinite bound on a summation or integral is a common shorthand for specifying a limit.


title: Public Universal Friend

text: The Public Universal Friend (born Jemima Wilkinson; November 29, 1752 – July 1, 1819) was an American preacher born in Cumberland, Rhode Island, to Quaker parents. After suffering a severe illness in 1776, the Friend claimed to have died and been reanimated as a genderless evangelist named the Public Universal Friend, and afterward shunned both birth name and gendered pronouns. In androgynous clothes, the Friend preached throughout the northeastern United States, attracting many followers who became the Society of Universal Friends.


title: Public Universal Friend

text: The Friend's theology was broadly similar to that of most Quakers. The Friend stressed free will, opposed slavery, and supported sexual abstinence. The most committed members of the Society of Universal Friends were a group of unmarried women who took leading roles in their households and community. In the 1790s, members of the Society acquired land in Western New York where they formed the town of Jerusalem near Penn Yan, New York. The Society of Universal Friends ceased to exist by the 1860s. Many writers have portrayed the Friend as a woman, and either a manipulative fraudster, or a pioneer for women's rights; others have viewed the Friend as transgender or non-binary and a figure in trans history.


title: Public Universal Friend

text: Jemima Wilkinson, who would later become the Public Universal Friend, was born on November 29, 1752, in Cumberland, Rhode Island, as the eighth child of Amy (or Amey, née Whipple) and Jeremiah Wilkinson, becoming the fourth generation of the family to live in America. The child was given the name Jemima after Jemima, one of the biblical Job's daughters. Jemima's great-grandfather, Lawrence Wilkinson, was an officer in the army of Charles I who had emigrated from England around 1650 and was active in colonial government. Jeremiah Wilkinson was a cousin of Stephen Hopkins, the colony's longtime governor and signer of the Declaration of Independence. Jeremiah attended traditional worship with the Society of Friends (the Quakers) at the Smithfield Meeting House. Early biographer David Hudson says that Amy was also a member of the Society for many years, while later biographer Herbert Wisbey finds no evidence of that, but quotes Moses Brown as saying the child was "born such" because of Jeremiah's affiliation. Amy died when Jemima was 12 or 13 in 1764, shortly after giving birth to a twelfth child.


title: Public Universal Friend

text: Jemima Wilkinson had fine black hair and eyes, and from an early age was strong and athletic, becoming an adept equestrian as a child, remaining so in adulthood, and liking spirited horses and ensuring that animals received good care. An avid reader, Wilkinson could quote long passages of the Bible and prominent Quaker texts from memory. Little else is reliably known about Wilkinson's childhood; some early accounts such as Hudson's describe Jemima Wilkinson as being fond of fine clothes and averse to labor, but there is no contemporaneous evidence of this and Wisbey considers it doubtful. Biographer Paul Moyer says it may have been invented to fit a then-common narrative that people who experienced dramatic religious awakenings were formerly profligate sinners.


title: Public Universal Friend

text: In the mid-1770s, Jemima Wilkinson began attending meetings in Cumberland with New Light Baptists who had formed as part of the Great Awakening and emphasized individual enlightenment, and stopped attending meetings of the Society of Friends— being disciplined for that in February 1776 and disowned by the Smithfield Meeting in August. Jemima Wilkinson's sister Patience was dismissed at the same time for having an illegitimate child; brothers Stephen and Jeptha had been dismissed by the pacifistic Society in May 1776 for training for military service. Amid these family disturbances and the broader ones of the American Revolutionary War, dissatisfied with the New Light Baptists and shunned by mainstream Quakers, Jemima Wilkinson faced much stress in 1776.


title: Public Universal Friend

text: In October 1776 Jemima Wilkinson contracted an epidemic disease, most likely typhus, and was bedridden and near death with a high fever. The future preacher's family summoned a doctor from Attleboro, six miles away, and neighbors kept up a death-watch at night. The fever broke after several days. The Friend later reported that Jemima Wilkinson had died, receiving revelations from God through two archangels who proclaimed there was "Room, Room, Room, in the many Mansions of eternal glory for Thee and for everyone". The Friend further said that Wilkinson's soul had ascended to heaven and the body had been reanimated with a new spirit charged by God with preaching his word, that of the "Publick Universal Friend", describing that name in the words of as "a new name which the mouth of the Lord hath named". The name referenced the designation the Society of Friends used for members who traveled from community to community to preach, "Public Friends". In the 18th and 19th centuries, some writers said that Wilkinson did briefly die during the illness, or even was dead for an extended time before rising dramatically from a coffin, while others suggested that the entire illness was feigned. Accounts by the doctor and other witnesses state that the illness was real, but none of them say that Wilkinson died.


title: Public Universal Friend

text: From that time on, the person formerly known as Jemima Wilkinson refused to answer to that name any longer, ignoring or chastising those who insisted on using it. Hudson says that when visitors asked if it was the name of the person they were addressing, the Friend simply quoted ("thou sayest it"). Identifying as neither male nor female, the Friend asked not to be referred to with gendered pronouns. Followers respected these wishes; they referred only to "the Public Universal Friend" or short forms such as "the Friend" or "P.U.F.", and many avoided gender-specific pronouns even in private diaries, while others used "he". When someone asked if the Friend was male or female, the preacher replied "I am that I am", saying the same thing to a man who criticized the Friend's manner of dress.


title: Public Universal Friend

text: The Friend dressed in a manner perceived to be either androgynous or masculine, in long, loose clerical robes which were most often black, and wore a white or purple kerchief or cravat around the neck like men of the time. The preacher did not wear a hair-cap indoors, like women of the era, and outdoors wore broad-brimmed, low-crowned beaver hats of a style worn by Quaker men. Accounts of the Friend's "feminine-masculine tone of voice" varied; some hearers described it as "clear and harmonious", or said the preacher spoke "with ease and facility", "clearly, though without elegance"; others described it as "grum and shrill", or like a "kind of croak, unearthly and sepulchral". The Friend was said to move easily, freely, and modestly, and was described by Ezra Stiles as "decent & graceful & grave".


title: Public Universal Friend

text: The Friend began to travel and preach throughout Rhode Island, Connecticut, Massachusetts, and Pennsylvania accompanied by brother Stephen and sisters Deborah, Elizabeth, Marcy, and Patience, all of whom were disowned by the Society of Friends. Early on, the Public Universal Friend preached that people needed to repent of their sins and be saved before an imminent Day of Judgment. According to Abner Brownell, the preacher predicted that the fulfillment of some prophecies of Revelation would begin around April 1780, 42 months after the Universal Friend began preaching, and interpreted New England's Dark Day in May 1780 as fulfillment of that prediction. According to a Philadelphia newspaper, later followers Sarah Richards and James Parker believed themselves to be the two witnesses mentioned in Revelation and accordingly wore sackcloth for a time.


title: Public Universal Friend

text: The Friend did not bring a Bible to worship meetings, which were initially held outdoors or in borrowed meeting houses, but preached long sections of the scriptures from memory. The meetings attracted large audiences, including some who formed a congregation of "Universal Friends", making the Friend the first American to found a religious community. These followers included roughly equal numbers of women and men who were predominantly under 40. Most were from Quaker backgrounds, though mainstream Quakers discouraged and disciplined members for attending meetings with the Friend. Indeed, the Society of Friends had disowned the Friend, disapproving of what William Savery considered "pride and ambition to distinguish [them]self from the rest of mankind". Free Quakers, disowned by the main Society of Friends for participating in the American War of Independence, were particularly sympathetic and opened meeting houses to the Universal Friends, appreciating that many of them had also sympathized with the Patriot cause, including members of the Friend's family.


title: Public Universal Friend

text: Popular newspapers and pamphlets covered the Friend's sermons in detail by the mid-1780s, with several Philadelphia newspapers being particularly critical; they fomented enough opposition that noisy crowds gathered outside each place the preacher stayed or spoke in 1788. Most papers focused more on the preacher's ambiguous gender than on theology, which was broadly similar to the teachings of most Quakers; one person who heard the Friend in 1788 said "from common report I expected to hear something out of the way in doctrine, which is not the case, in fact [I] heard nothing but what is common among preachers" in mainstream Quaker churches. The Friend's theology was so similar to that of the mainstream Quakers' that one of two published works associated with the preacher was a plagiarism of Isaac Penington's "Works" because, according to Abner Brownell, the Friend felt that the sentiments would have more resonance if republished in the name of the Universal Friend. The Universal Friends also used language similar to that of the Society of Friends, using "thee" and "thou" instead of singular "you".


title: Public Universal Friend

text: The Public Universal Friend rejected the ideas of predestination and election, held that anyone regardless of gender could gain access to God's light and that God spoke directly to individuals who had free will to choose how to act and believe, and believed in the possibility of universal salvation. Calling for the abolition of slavery, the Friend persuaded followers who held people in slavery to free them. Several members of the congregation of Universal Friends were black, and they acted as witnesses for manumission papers. The Friend preached humility and hospitality towards everyone; kept religious meetings open to the public, and housed and fed visitors, including those who came only out of curiosity and indigenous people, with whom the preacher generally had a cordial relationship. The Friend had few personal possessions, mostly given by followers, and never held any real property except in trust.


title: Public Universal Friend

text: The Friend preached sexual abstinence and disfavored marriage, but did not see celibacy as mandatory and accepted marriage, especially as preferable to breaking abstinence outside of wedlock. Most followers did marry, but the portion who did not was significantly above the national average of the time. The preacher also held that women should "obey God rather than men", and the most committed followers included roughly four dozen unmarried women known as the Faithful Sisterhood who took on leading roles of the sort which were often reserved to men. The portion of households headed by women in the Society's settlements (20%) was much higher than in surrounding areas.


title: Public Universal Friend

text: Around 1785, the Friend met Sarah and Abraham Richards. The Richards' unhappy marriage ended in 1786, when Abraham died on a visit to the Friend. Sarah, together with her infant daughter, took up residence with the Friend, adopted a similarly androgynous hairstyle, dress, and mannerisms (as did a few other close female friends), and came to be called Sarah Friend. The Friend entrusted Richards with holding the society's property in trust, and sent her to preach in one part of the country when the Friend was in another. Richards had a large part in planning and building the house in which she and the preacher lived in the town of Jerusalem, and when she died in 1793, she left her child to the Friend's care.


title: Public Universal Friend

text: In October 1794, the Friend and several followers dined with Thomas Morris (son of financier Robert Morris) in Canandaigua at the invitation of Timothy Pickering, and accompanied him to talks with the Iroquois aimed at producing the Treaty of Canandaigua. With Pickering's permission and an interpreter, the Friend gave a speech to the US government officials and Iroquois chiefs about "the Importance of Peace & Love", which was liked by the Iroquois.


title: Public Universal Friend

text: In the mid-1780s, the Universal Friends began to plan a town for themselves in western New York. By late 1788, vanguard members of the Society had established a settlement in the Genesee River area; by March 1790, it was ready enough that the rest of the Universal Friends set out to join it, making it the largest non-Native community in western New York. However, problems arose. James Parker spent three weeks in 1791 petitioning the governor and land office of New York on behalf of the Society to get a title to the land that the Friends had settled, but while most of the buildings and other improvements that the Universal Friends made were to the east of the initial Preemption Line and thus in New York, when the line was resurveyed in 1792 at least 25 homes and farms were now west of it, outside the area granted by New York, and residents were forced to repurchase their lands from the Pulteney Association. The town, which had been known as the Friend's Settlement, therefore came to be called The Gore.


title: Public Universal Friend

text: Furthermore, the lands were in the tract on which Phelps and Gorham defaulted which was resold to financier Robert Morris and then to the Pulteney Association, absentee British speculators. Each change of hands drove prices higher, as did an influx of new settlers attracted by the Society's improvements to the area. The community lacked a solid title to enough land for all its members, and some left. Others wanted to profit by taking ownership of the land for themselves, including Parker and William Potter. To address the first of these issues, members of the Society of Universal Friends had secured some alternative sites. Abraham Dayton acquired a large area of land in Canada from Governor John Graves Simcoe, though Sarah Richards persuaded the Friend not to move so far. Separately, Thomas Hathaway and Benedict Robinson had purchased a site in 1789 along a creek which they named Brook Kedron that emptied into the Crooked Lake (Keuka Lake). The new town which the Universal Friends began there came to be called Jerusalem.


title: Public Universal Friend

text: The second issue, however, came to a head in the fall of 1799. Judge William Potter, Ontario County magistrate James Parker, and several disillusioned former followers led several attempts to arrest the Friend for blasphemy, which some writers argue was motivated by disagreements over land ownership and power. An officer tried to seize the Friend while riding with Rachel Malin in the Gore, but the Friend, a skilled horse-rider, escaped. The officer and an assistant later tried to arrest the preacher at home in Jerusalem, but the women of the house drove the men off and tore their clothes. A third attempt was carefully planned by a posse of 30 men who surrounded the home after midnight, broke down the door with an ax, and intended to carry the preacher off in an oxcart. A doctor who had come with the posse stated that the Friend was in too poor a state of health to be moved, and they made a deal that the Friend would appear before an Ontario county court in June 1800, but not before Justice Parker. When the Friend appeared before the court, it ruled that no indictable offense had been committed, and invited the preacher to give a sermon to those in attendance.


title: Public Universal Friend

text: The Public Universal Friend's health had been declining since the turn of the century; by 1816 the preacher had begun to suffer from a painful edema, but continued to receive visitors and give sermons. The Friend gave a final regular sermon in November 1818 and preached for the last time at the funeral of sister Patience Wilkinson Potter in April 1819.


title: Public Universal Friend

text: The Friend died on July 1, 1819; the congregation's death book records "25 minutes past 2 on the Clock, The Friend went from here." In accordance with the Friend's wishes, only a regular meeting and no funeral service was held afterwards. The body was placed in a coffin with an oval glass window set in top, interred four days after death in a thick stone vault in the cellar of the Friend's house. Several years later, the coffin was removed and buried in an unmarked grave in accordance with the preacher's preference. Obituaries appeared in papers throughout the eastern United States. Close followers remained faithful, but they too died over time; the congregation's numbers dwindled due to their inability to attract new converts amid a number of legal and religious disagreements. The Society of Universal Friends disappeared by the 1860s.


title: Public Universal Friend

text: The Friend's Home and temporary burial chamber stands in the town of Jerusalem, and it is included on the National Register of Historic Places. It is believed to be located on the same branch of Keuka Lake as the birthplace of Seneca chief Red Jacket, but his birthplace is disputed. The Yates County Genealogical and Historical Society's museums in Penn Yan exhibit the Friend's portrait, Bible, carriage, hat, saddle, and documents from the Society of Universal Friends. As late as the 1900s, inhabitants of Little Rest, Rhode Island, called a species of solidago "Jemima weed" because its appearance in the town coincided with the preacher's first visit to the area in the 1770s.


title: Public Universal Friend

text: The Friend and followers were pioneers of the area between Seneca and Keuka lakes. The Society of Universal Friends erected a grain mill in Dresden.


title: Public Universal Friend

text: Although the Public Universal Friend identified as genderless, neither a man nor a woman, many writers have portrayed the preacher as a woman, and either a fraudulent schemer who deceived and manipulated followers or a pioneering leader who founded several towns in which women were empowered to take on roles often reserved to men. The first view was taken by many writers in the 18th and 19th centuries, including David Hudson, whose hostile and inaccurate biography (written to influence a court case over the Society's land) was long influential. These writers circulated myths of the Friend despotically bossing followers around or banishing them for years, making married followers divorce, taking their property, or even attempting and failing to raise the dead or walk on water; there is no contemporaneous evidence for these stories, and people who knew the Friend, including some who were never followers, said the rumors were false.


title: Public Universal Friend

text: Another story began at a 1787 meeting, after which Sarah Wilson said Abigail Dayton tried to strangle Wilson while she slept but choked her bedmate Anna Steyers by mistake. Steyers denied anything had happened, and others present attributed Wilson's fears to a nightmare. Nevertheless, Philadelphia papers printed an embellished version of the accusation and several follow-ups, with critics alleging the attack must have had the Friend's approval, and the story eventually morphing into one in which the Friend (who was in a different state at the time) strangled Wilson. One widespread allegation which sparked much hostility was the accusation that the preacher claimed to be Jesus; the Friend and the Universal Friends repeatedly denied this accusation.


title: Public Universal Friend

text: Modern writers have often portrayed the Friend as a pioneer, an early figure in the history of women's rights (a view taken by Susan Juster and Catherine Brekus) or in transgender history (a view explored by Scott Larson and Rachel Hope Cleves). Historian Michael Bronski says that the Friend would not have been called transgender or transvestite "by the standards and the vocabulary" of the time, but has called the Friend a "transgender evangelist". Juster calls the Friend a "spiritual transvestite", and says that followers considered the Friend's androgynous clothing congruent with the genderless spirit which they believed animated the preacher.


title: Public Universal Friend

text: Juster and others state that, to followers, the Friend may have embodied Paul's statement in that "there is neither male nor female" in Christ. Catherine Wessinger, Brekus, and others state that the Friend defied the idea of gender as binary and as natural and essential or innate, though Brekus and Juster argue that the Friend nonetheless reinforced views of male superiority by "dressing like a man" and repeatedly insisting on not being a woman. Scott Larson, disagreeing with narratives that place the Public Universal Friend into the gender binary as a woman, writes that the Friend can be understood as a chapter in trans history "before 'transgender. Bronski cites the Friend as a rare instance of an early American publicly identifying as non-binary.


title: Public Universal Friend

text: T. Fleischmann's essay "Time Is the Thing the Body Moves Through" examines the Friend's narrative with an eye to the colonizing nature of evangelism in the US, viewing it as "a way to think through the limitations of imagination as a white settler". The Public Universal Friend was also featured in an episode of the NPR radio program and podcast "Throughline".


title: The Day of the Triffids

text: The Day of the Triffids is a 1951 post-apocalyptic novel by the English science fiction author John Wyndham. After most people in the world are blinded by an apparent meteor shower, an aggressive species of plant starts killing people. Although Wyndham had already published other novels using other pen name combinations drawn from his real name, this was the first novel published as "John Wyndham".


title: The Day of the Triffids

text: The story has been made into the 1962 feature film of the same name, three radio drama series (in 1957, 1968 and 2001) and two TV series (in 1981 and 2009). It was nominated for the International Fantasy Award in 1952, and in 2003 the novel was listed on the BBC's survey The Big Read.


title: The Day of the Triffids

text: It was the inspiration for the zombie movie "28 Days Later". In 2021, the novel was one of six classic science fiction novels by British authors selected by Royal Mail to feature on a series of UK postage stamps.


title: The Day of the Triffids

text: The protagonist is Bill Masen, a biologist who has made his living working with triffids—tall, venomous, carnivorous plants capable of locomotion. Due to his background, Masen suspects they were bioengineered in the U.S.S.R. and accidentally released into the wild. Because of the excellent industrial quality of an oil produced by and obtained from the triffids, there is heavy triffid cultivation around the world.


title: The Day of the Triffids

text: The narrative begins with Bill Masen in hospital, his eyes bandaged after having been splashed with triffid poison from a stinger. During his recovery he is told of an unexpected green meteor shower. The next morning, he learns that the light from the unusual display has rendered any who watched it blind (later in the book, Masen speculates that the "meteor shower" may have been orbiting satellite weapons, triggered accidentally). After unbandaging his eyes he finds the hospital in chaos, with staff and patients without sight. He wanders through a chaotic London full of blind inhabitants and slowly becomes enamoured of wealthy novelist Josella Playton, whom he rescues after discovering her being forcibly used as a guide by a blind man. Intrigued by a single light on top of the Senate House in an otherwise darkened London, Bill and Josella discover a group of sighted survivors led by a man named Beadley, who plans to establish a colony in the countryside. They decide to join the group.


title: The Day of the Triffids

text: The polygamy implicit in Beadley's scheme appalls some group members, especially the religious Miss Durrant—but before this schism can be dealt with, a man named Wilfred Coker stages a fire at the university and kidnaps a number of sighted individuals, including Bill and Josella. They are each chained to a blind person and assigned to lead a squadron of the blind, collecting food and other supplies, all the while beset by escaped triffids and rival scavengers.


title: The Day of the Triffids

text: Soon Masen's followers begin to fall sick and die of an unknown disease. When he wakes one morning to find the survivors have left him, he returns to the University Tower to seek Josella but his only lead is an address left behind by Beadley's group. Joined by a repentant Coker, Masen drives to the address, a country estate called Tynsham in Wiltshire. He finds part of the Beadley group, now led by Miss Durrant, who eventually tells him that Beadley went to Beaminster, in Dorset, a few days before he arrived. There has been no sign of Josella.


title: The Day of the Triffids

text: Masen and Coker decide to follow Beadley to Dorset. They find small groups of blind and sighted people along the way but no trace of Beadley. Eventually they decide to separate, Coker returning to help at Tynsham, while Masen heads for the Sussex Downs after remembering a remark Josella made about friends she had there.


title: The Day of the Triffids

text: En route, Masen rescues a young sighted girl named Susan, whom he finds trapped alone at home, while her young brother lies dead in the garden, killed by a triffid. He buries the boy and takes Susan with him. A few days later, during a night of heavy rain, they see a faint light in the distance. Upon reaching it, they discover Josella and her friends.


title: The Day of the Triffids

text: They attempt to establish a self-sufficient colony in Sussex with some success but they are constantly under threat from the triffids, which mass around the fenced exterior. Several years pass, until one day a representative of Beadley's faction lands a helicopter in their yard and reports that his group has established a colony on the Isle of Wight. Durrant's talk of Beaminster was a deliberate attempt to throw Masen off on his journey to find Beadley. While Bill and the others are reluctant to leave their own settlement, the group decide to see the summer out in Sussex before moving to the Isle of Wight.


title: The Day of the Triffids

text: Their plans are hurried by the arrival of the militaristic representatives of a new despotic and self-appointed government, who arrive in an armoured car. Masen recognises the leader as a ruthless young man he had encountered on a scavenging expedition in London whom he had watched cold-bloodedly execute one of his own party who had fallen ill. The latter plans to give Masen a large number of blind people to care for, and use on the farm as slave labour; he will also take Susan as hostage. Feigning agreement, Masen's group throw a party, during which they encourage the visitors to get drunk. Creeping out of the house whilst the visitors are fast asleep, they disable the armoured car by pouring honey into the fuel tank and drive through the gates, leaving them open for the triffids to pour in. The novel ends with Masen's group on the Isle of Wight, determined one day to destroy the triffids and reclaim their world.


title: The Day of the Triffids

text: In the United States, Doubleday & Company holds the 1951 copyright. A condensed version of the book also was serialized in "Collier's" magazine in January and February 1951. An unabridged paperback edition was published in the late 1960s, in arrangement with Doubleday, under the Crest Book imprint of Fawcett Publications World Library.


title: The Day of the Triffids

text: Wyndham frequently acknowledged the influence of H. G. Wells' "The War of the Worlds" (1897) on "The Day of the Triffids"— Wells's working title had been "The Day of the Tripods".


title: The Day of the Triffids

text: The triffids are related, in some editions of the novel, to brief mention of the theories of the Soviet agronomist Trofim Lysenko, a proponent of Lamarckism who eventually was thoroughly debunked. "In the days when information was still exchanged Russia had reported some successes. Later, however, a cleavage of methods and views had caused biology there, under a man called Lysenko, to take a different course" (Chapter 2). Lysenkoism at the time of the novel's creation was still being defended by some prominent international Stalinists."


title: The Day of the Triffids

text: During the Blitz, Wyndham was a fire watcher and later member of the Home Guard. He witnessed the destruction of London from the rooftops of Bloomsbury. He described many scenes and incidents, including the uncanny silence of London on a Sunday morning after a heavy bombardment, in letters to his long-term partner Grace Wilson. These found their way into "The Day of the Triffids".


title: The Day of the Triffids

text: The book has been praised by other science fiction writers. Karl Edward Wagner cited "The Day of the Triffids" as one of the thirteen best science-fiction horror novels. Arthur C. Clarke called it an "immortal story". Anthony Boucher and J. Francis McComas praised it, saying: "rarely have the details of [the] collapse been treated with such detailed plausibility and human immediacy, and never has the collapse been attributed to such an unusual and terrifying source". Forrest J. Ackerman wrote in "Astounding Science Fiction" that "Triffids" "is extraordinarily well carried out, with the exception of a somewhat anticlimactic if perhaps inevitable conclusion".


title: The Day of the Triffids

text: Brian Aldiss coined the disparaging phrase cosy catastrophe to describe the subgenre of post-war apocalyptic fiction in which society is destroyed save for a handful of survivors, who are able to enjoy a relatively comfortable existence. He singled out "The Day of the Triffids" as an example and described "Triffids" as "totally devoid of ideas". However, some more recent critics have argued against this view. Margaret Atwood wrote: "one might as well call World War II—of which Wyndham was a veteran—a 'cozy' war because not everyone died in it".


title: The Day of the Triffids

text: John Clute commented that the book was regularly chosen for school syllabuses, as it was "safe". Robert M. Philmus called it derivative of better books by H. G. Wells. Groff Conklin, reviewing the novel's first publication, characterised it as "a good run-of-the-mill affair" and "pleasant reading... provided you aren't out hunting science fiction masterpieces".


title: The Day of the Triffids

text: According to director Danny Boyle, the opening hospital sequence of "The Day of the Triffids" inspired Alex Garland to write the screenplay for "28 Days Later" (2002).


title: The Day of the Triffids

text: The 2012 short story "How to Make a Triffid" by Kelly Lagor includes discussions of the possible genetic pathways that could be manipulated to engineer the triffids.


title: The Day of the Triffids

text: "The Day of the Triffids" touches on mankind's advances in science and technology as a possible contributor to the collapse of society that's depicted in the novel.


title: The Day of the Triffids

text: In a master's thesis entitled "Social Critique in the Major Novels of John Wyndham: Civilization's Secrets and Nature's Truths", Michael Douglas Green writes about other scientific contributions to the novel's apocalypse:


title: The Day of the Triffids

text: Critics have highlighted the parallels between the triffids and the decolonization that took place in Europe after 1945. In an essay entitled "The Politics of Post-Apocalypse: Ideologies on Trial in John Wyndham's "The Day of the Triffids"", literary critic Jerry Määttä writes:


title: The Day of the Triffids

text: Robert Yeates, in his essay "Gender and Ethnicity in Post-Apocalyptic Suburbia", proposes another connection to colonialism:


title: The Day of the Triffids

text: At the time of the novel's writing there was an emerging welfare state in Great Britain after the formation of the Attlee ministry. Coker's forced shackling of sighted people to the blind echoes the sentiments that some middle-class British citizens felt in the wake of the changes introduced by the Labour party after their 1945 election victory.


title: The Day of the Triffids

text: The novel frequently brings into question the utility of individualism during the apocalypse. Colin Manlove highlights this phenomenon in his essay "Everything Slipping Away: John Wyndham's "The Day of the Triffids"":


title: The Day of the Triffids

text: Simon Clark wrote a sequel "The Night of the Triffids" (2001). This is set 25 years after Wyndham's book, and focuses on the adventures of Bill Masen's son David, who travels to New York, USA. Big Finish Productions adapted it as an audio play in 2014. The dramatisation featuring Sam Troughton was later broadcast on BBC Radio 4 Extra in June 2016.


title: The Day of the Triffids

text: In 2020, English science fiction and fantasy author John Whitbourn published a sequel, entitled "The Age of the Triffids". Set in the Isle of Wight "Colony" in the lead-up to the Millennium, it details the rallying of survivors from across Britain for one last attempt to defeat the triffid threat. For copyright reasons, the book is not for sale outside Canada and New Zealand.


title: Kate Nash

text: Nash launched her music career in 2005. Her 2007 single "Foundations" became a hit and brought her to public attention in the UK. Her debut album, "Made of Bricks", peaked at No. 1 in the UK and was a moderate international success. Nash subsequently won the award for Best British Female Artist at the 2008 Brit Awards. Her second studio album, "My Best Friend Is You", was released in 2010 and reached the top 10 in the UK and Germany. After her departure from a major label, Nash self-released her third studio album, "Girl Talk", in 2013, but it failed to match the commercial success of her previous records. Her fourth and most recent studio album, "Yesterday Was Forever", was also released independently in 2018, funded by her fans via a Kickstarter campaign.


title: Kate Nash

text: Aside from music, Nash has appeared in films such as the drama "Greetings from Tim Buckley" (2012), the comedy "Powder Room" (2013), and the comedy-drama "Syrup" (2013). She played Rhonda "Britannica" Richardson in the Netflix comedy-drama series "GLOW" (2017–2019). She is also a feminist activist who campaigns against gender inequality.


title: Kate Nash

text: Kate Marie Nash was born in the London Borough of Harrow in London on 6 July 1987, the second of three daughters born to an English father and Irish mother. Her father, Steve, is a systems analyst, while her mother, Marie (née Walsh), was a hospice nurse. She learned to play the piano at an early age. At 18, she underwent cardiac radiofrequency ablation in order to eliminate tachycardia. The surgery subsequently inspired her song "Death Proof". She attended the BRIT School and originally wanted to study acting, but turned to music after she was rejected from several drama colleges and universities, including the Bristol Old Vic Theatre School. Prior to her musical career, she worked in a River Island shop and a Nando's restaurant.


title: Kate Nash

text: Nash embarked on a musical career in 2005, when she started recording after falling down the stairs and breaking her foot, which left her homebound. She started performing live, holding her first shows in pubs, at open mic nights, and an anti-folk festival in Brighton. After several gigs, she uploaded her music to MySpace where she secured a manager and found exposure thanks to support from Lily Allen. Her debut single, featuring songs "Caroline's a Victim" and "Birds", was recorded and produced in Iceland by Valgeir Sigurðsson, and released through Moshi Moshi Records in February 2007. The release was limited to 2,000 copies and available only on 7-inch vinyl. Due to demand, another 1,000 copies were made and these also sold out. CD promo copies were produced for distribution to the press and DJs and are occasionally available for sale. The music video for "Caroline's a Victim" was directed by Kinga Burza and received airplay on MTV2. The song was then included on the CD "Moshi Moshi Singles Compilation" and the single's B-side, "Birds", later featured on Nash's debut album. Both tracks have also been released on digital music platforms.


title: Kate Nash

text: In April 2007, Nash was signed to the Polydor offshoot Fiction Records and the following month made her official TV performance debut on "Later... with Jools Holland". Her second single, "Foundations", which she co-wrote with producer Paul Epworth, was released by Fiction on 18 June 2007, and reached number two in the official UK Singles Chart. Following this success, the label announced plans to bring forward the release of Nash's debut album "Made of Bricks" to 6 August 2007. Produced by Paul Epworth, the album included many of the tracks she had been performing during her two nationwide tours. "Made of Bricks" was leaked to filesharing networks a few days before its official commercial release and subsequently received mixed reviews; "The Independent" described it as being in "pole position for worst album of the year", while a BBC review called it "an album of surprising verve and variety". It proved, however, to be commercially successful when it entered and peaked on the UK Albums Chart at number 1, and stayed in the chart for over forty consecutive weeks.


title: Kate Nash

text: During mid-2007, Nash performed at numerous festivals, including the Wireless Festival, Bestival, Electric Gardens, Glastonbury, Latitude, Reading and Leeds, Oxegen and T in the Park. Throughout late 2007 and early 2008, she released three more singles from "Made of Bricks". "Mouthwash" and "Pumpkin Soup" both made the Top 40 in the UK Singles Chart. Although her fifth single "Merry Happy" didn't chart well in the UK, the song enjoyed minor success in other countries, including the United States and Canada. "Made of Bricks" peaked at number 36 on the US "Billboard" 200 chart in January 2008. It would later be certified Platinum in the UK and Gold in Germany. In February 2008, Nash was honoured with the Best British Female Solo Artist award at the 2008 Brit Awards. She also won the Q Award for Breakthrough Artist and the NME Award for Best Solo Artist. Nash embarked on her first tour in Australia and the US in 2008 and opened the 2008 Glastonbury Festival.


title: Kate Nash

text: In March 2009, Nash became one of the founding members of Featured Artists' Coalition, a nonprofit organization and lobbying group, and revealed that she was in the early stages of recording her second album. She was introduced by her boyfriend Ryan Jarman to Bernard Butler, the producer of Duffy's debut album "Rockferry" and a former guitarist for Suede. The pair worked on eight songs at RAK Studios in the summer that year. As a side project in late 2009, Kate joined a punk band called The Receeders where she played bass guitar, with Jon Jackson and Brett Alaimo. In December, the band played a live gig at 93 Feet East.


title: Kate Nash

text: In January 2010, Nash revealed that the album was complete, and the following month the song "I Just Love You More" was made available for free download from her official website. The first official single from the album was "Do-Wah-Doo", which was released on 12 April 2010, to a moderate chart success. Nash's second studio album "My Best Friend Is You" was released a week later and was met with generally positive reviews. The sound was described as having a girl group approach, influenced by a wide variety of genres, from Wall of Sound, Motown to no wave and riot grrrl. The album reached the top 10 on the charts in the UK and Germany, and met with moderate success elsewhere. Two further singles from the album, "Kiss That Grrrl" and "Later On", were released in 2010, but failed to chart. To promote the record, the singer embarked on a tour, beginning with nine dates in North America in late April, with the all-female travelling festival Lilith Fair. Her opening act was Supercute!, a psychedelic pop teen girl trio from New York City. She also took part in the 2010 V Festival. In August Nash performed in Australia at Melbourne's Corner Hotel and Sydney's Metro Theatre. In February 2011, her concerts in Rio de Janeiro and São Paulo were the first contact with her Brazilian fans. The singer declared the Rio show "the best concert of her life" and "the happiest place she has ever been".


title: Kate Nash

text: After Fiction Records terminated her contract, Nash launched her own record label, Have 10p Records. Indie act Brigitte Aphrodite (who had toured with Kate on many occasions) was the first artist signed to the label and released the debut single "I Dream Myself Awake" in 2011. Nash also appeared in Supercute!'s music video "Dumb Dumbs" and helped to produce their first album which eventually could not be released due to the band's split-up. Later in 2011, she launched the Kate Nash's Rock 'n' Roll for Girls After School Music Club as a platform to inspire teenage girls to get into songwriting and making their own music, due to the shortage of female artists in the UK. On her UK tour that year, Nash promoted the initiative in schools such as the City of Portsmouth Girls' School, Woodchurch High School and John Madejski Academy.


title: Kate Nash

text: In February 2012, Nash wrote and recorded a song with some of the Occupy London protesters camping outside the St Paul's Cathedral, following workshops led by her and Sam Duckworth of Get Cape. Wear Cape. Fly. She contributed the song "My Chinchilla" to the Nardwuar and The Evaporators' album "Busy Doing Nothing!". She also collaborated with Brisbane-based band The Thin Kids which resulted in the single "The Thin Kids Theme" released on her label and wrote the song "I Am Me" with Willow Smith, which was released later in 2012.