Week

A week is a time unit equal to seven days. It is the standard time period used for cycles of rest days in most parts of the world, mostly alongside—although not strictly part of—the Gregorian calendar.
In many languages, the days of the week are named after classical planets or gods of a pantheon. In English, the names are Monday, Tuesday, Wednesday, Thursday, Friday, Saturday and Sunday, then returning to Monday. Such a week may be called a "planetary week". This arrangement is similar to a week in the New Testament in which the seven days are simply numbered with the first day being a Christian day of worship (aligned with Sunday, offset from ISO 8601 by one day) and the seventh day being a sabbath day (Saturday).
While, for example, the United States, Canada, Brazil, Japan and other countries consider Sunday as the first day of the week, and while the week begins with Saturday in much of the Middle East, the international ISO 8601 standard and most of Europe has Monday as the first day of the week. The ISO standard includes the ISO week date system, a numbering system for weeks within a given year, where each week starting on a Monday is associated with the year that contains that week's Thursday (so that if a year starts in a long weekend Friday–Sunday, week number one of the year will start after that, and if, conversely, a year ends on a Monday, Tuesday or Wednesday, the last days of the year are counted as part of week 1 of the following year). ISO 8601 assigns numbers to the days of the week, running from 1 for Monday through 7 for Sunday.
The term "week" is sometimes expanded to refer to other time units comprising a few days, such as the nundinal cycle of the ancient Roman calendar, the "work week", or "school week" referring only to the days spent on those activities.
Name.
The English word "week" comes from the Old English "wice", ultimately from a Common Germanic ', from a root ' "turn, move, change". The Germanic word probably had a wider meaning prior to the adoption of the Roman calendar, perhaps "succession series", as suggested by Gothic "wikō" translating "taxis" "order" in Luke 1:8.
The seven-day week is named in many languages by a word derived from "seven". The archaism sennight ("seven-night") preserves the old Germanic practice of reckoning time by nights, as in the more common "fortnight" ("fourteen-night"). Hebdomad and hebdomadal week both derive from the Greek "hebdomás" (, "a seven"). Septimana is cognate with the Romance terms derived from Latin "septimana" ("a seven").
Slavic has a formation "*tъ(žь)dьnь" (Serbian , Croatian tjedan, Ukrainian , Czech "týden", Polish "tydzień"), from "*tъ" "this" + "*dьnь" "day". Chinese has 星期, as it were "planetary time unit".
Definition and duration.
A week is defined as an interval of exactly seven days, so that, except at daylight saving time transitions or leap seconds,
With respect to the Gregorian calendar:
In a Gregorian mean year, there are 365.2425 days, and thus exactly or 52.1775 weeks (unlike the Julian year of 365.25 days or ≈ 52.1786 weeks, which cannot be represented by a finite decimal expansion). There are exactly 20,871 weeks in 400 Gregorian years, so was a just as was .
Relative to the path of the Moon, a week is 23.659% of an average lunation or 94.637% of an average quarter lunation.
Historically, the system of dominical letters (letters A to G identifying the weekday of the first day of a given year) has been used to facilitate calculation of the day of week.
The day of the week can be easily calculated given a date's Julian day number (JD, i.e. the integer value at noon UT):
Adding one to the remainder after dividing the Julian day number by seven (JD "modulo" 7 + 1) yields that date's ISO 8601 day of the week. For example, the Julian day number of is . Calculating yields , corresponding to .
Days of the week.
The days of the week were named for the classical planets. This naming system persisted alongside an "ecclesiastical" tradition of numbering the days in ecclesiastical Latin beginning with "Dominica" (the Lord's Day) as the first day. The Greco-Roman gods associated with the classical planets were rendered in their "interpretatio germanica" at some point during the late Roman Empire, yielding the Germanic tradition of names based on indigenous deities.
The ordering of the weekday names is not the classical order of the planets (by distance in the planetary spheres model, nor, equivalently, by their apparent speed of movement in the night sky). Instead, the planetary hours systems resulted in succeeding days being named for planets that are three places apart in their traditional listing. This characteristic was apparently discussed in Plutarch in a treatise written in c. AD 100, which is reported to have addressed the question of "Why are the days named after the planets reckoned in a different order from the actual order?" (the text of Plutarch's treatise has been lost).
An ecclesiastical, non-astrological, system of numbering the days of the week was adopted in Late Antiquity. This model also seems to have influenced (presumably via Gothic) the designation of Wednesday as "mid-week" in Old High German ("mittawehha") and Old Church Slavonic (срѣда). Old Church Slavonic may have also modeled the name of Monday, понєдѣльникъ, after the Latin "feria Secunda". The ecclesiastical system became prevalent in Eastern Christianity, but in the Latin West it remains extant only in modern Icelandic, Galician, and Portuguese.
History.
Ancient Near East.
The earliest evidence of an astrological significance of a seven-day period is connected to Gudea, the priest-king of Lagash in Sumer during the Gutian dynasty (about 2100 BCE), who built a seven-room temple, which he dedicated with a seven-day festival. In the flood story of the Assyro-Babylonian Epic of Gilgamesh, the storm lasts for seven days, the dove is sent out after seven days, and the Noah-like character of Utnapishtim leaves the ark seven days after it reaches the firm ground. 
Counting from the new moon, the Babylonians celebrated the 7th, 14th, 21st and 28th as "holy days", also called "evil days" (meaning "unsuitable" for prohibited activities). On these days, officials were prohibited from various activities and common men were forbidden to "make a wish", and at least the 28th was known as a "rest day".
On each of them, offerings were made to a different god and goddess.
In a frequently-quoted suggestion going back to the early 20th century, the Hebrew "Sabbath" is compared to the Sumerian "sa-bat" "mid-rest", a term for the full moon. The Sumerian term has been reconstructed as rendered "Sapattum" or "Sabattum" in Babylonian, possibly present in the lost fifth tablet of the Enûma Eliš, tentatively reconstructed "[Sa]bbath shalt thou then encounter, mid[month]ly".
It is possible that the Hebrew seven-day week is based on the Babylonian tradition, although going through certain adaptations. George Aaron Barton speculated that the seven-day creation account of Genesis is connected to the Babylonian creation epic, Enûma Eliš, which is recorded on seven tablets.
Judaism.
A continuous seven-day cycle that runs throughout history without reference to the phases of the moon was first practiced in Judaism, dated to the 6th century BC at the latest.
There are several hypotheses concerning the origin of the biblical seven-day cycle.
Friedrich Delitzsch and others suggested that the seven-day week being approximately a quarter of a lunation is the implicit astronomical origin of the seven-day week, and indeed the Babylonian calendar used intercalary days to synchronize the last week of a month with the new moon. According to this theory, the Jewish week was adopted from the Babylonians while removing the moon-dependency.
However, Niels-Erik Andreasen, Jeffrey H. Tigay, and others claimed that the Biblical Sabbath is mentioned as a day of rest in some of the earliest layers of the Pentateuch dated to the 9th century BC at the latest, centuries before the Babylonian exile of Judah. They also find the resemblance between the Biblical Sabbath and the Babylonian system to be weak. Therefore, they suggested that the seven-day week may reflect an independent Israelite tradition. Tigay writes:
It is clear that among neighboring nations that were in position to have an influence over Israel – and in fact which did influence it in various matters – there is no precise parallel to the Israelite Sabbatical week. This leads to the conclusion that the Sabbatical week, which is as unique to Israel as the Sabbath from which it flows, is an independent Israelite creation.
The seven-day week seems to have been adopted, at different stages, by the Persian Empire, in Hellenistic astrology, and (via Greek transmission) in Gupta India and Tang China. 
The Babylonian system was received by the Greeks in the 4th century BC (notably via Eudoxus of Cnidus). However, the designation of the seven days of the week to the seven planets is an innovation introduced in the time of Augustus. The astrological concept of planetary hours is rather an original innovation of Hellenistic astrology, probably first conceived in the 2nd century BC.
The seven-day week was widely known throughout the Roman Empire by the 1st century AD, along with references to the Jewish Sabbath by Roman authors such as Seneca and Ovid. When the seven-day week came into use in Rome during the early imperial period, it did not immediately replace the older eight-day nundinal system. The nundinal system had probably fallen out of use by the time Emperor Constantine adopted the seven-day week for official use in CE 321, making the Day of the Sun () a legal holiday.
Achaemenid period.
The Zoroastrian calendar follows the Babylonian in relating the 7th, 14th, 21st, and 28th of the month to Ahura Mazda.
The forerunner of all modern Zoroastrian calendars is the system used to determine dates in the Persian Empire, adopted from the Babylonian calendar by the 4th century BC.
Frank C. Senn in his book "Christian Liturgy: Catholic and Evangelical" points to data suggesting evidence of an early continuous use of a seven-day week; referring to the Jews during the Babylonian captivity in the 6th century BC, after the destruction of the Temple of Solomon.
While the seven-day week in Judaism is tied to Creation account in the Book of Genesis in the Hebrew Bible (where God creates the heavens and the earth in six days and rests on the seventh; , in the Book of Exodus, the fourth of the Ten Commandments is to rest on the seventh day, "Shabbat", which can be seen as implying a socially instituted seven-day week), it is not clear whether the Genesis narrative predates the Babylonian captivity of the Jews in the 6th century BC. At least since the Second Temple period under Persian rule, Judaism relied on the seven-day cycle of recurring Sabbaths.
Tablets from the Achaemenid period indicate that the lunation of 29 or 30 days basically contained three seven-day weeks, and a final week of eight or nine days inclusive, breaking the continuous seven-day cycle.
The Babylonians additionally celebrated the 19th as a special "evil day", the "day of anger", because it was roughly the 49th day of the (preceding) month, completing a "week of weeks", also with sacrifices and prohibitions.
Difficulties with Friedrich Delitzsch's origin theory connecting Hebrew "Shabbat" with the Babylonian lunar cycle include reconciling the differences between an unbroken week and a lunar week, and explaining the absence of texts naming the lunar week as "Shabbat" in any language.
Hellenistic and Roman era.
In Jewish sources by the time of the Septuagint, the term "Sabbath" (Greek "Sabbaton") by synecdoche also came to refer to an entire seven-day week, the interval between two weekly Sabbaths.
Jesus's parable of the Pharisee and the Publican (Luke 18:12) describes the Pharisee as fasting "twice in the week" (Greek ).
Days of the week are called "days of the sabbath" in the Hebrew language. In the account of the women finding the tomb empty, they are described as coming there , though modern translations often substitute "week" for "sabbath".
The ancient Romans traditionally used the eight-day nundinum but, after the Julian calendar had come into effect in 45 BC, the seven-day week came into increasing use. For a while, the week and the nundinal cycle coexisted, but by the time the week was officially adopted by Constantine in AD 321, the nundinal cycle had fallen out of use. The association of the days of the week with the Sun, the Moon and the five planets visible to the naked eye dates to the Roman era (2nd century).
The continuous seven-day cycle of the days of the week can be traced back to the reign of Augustus; the first identifiable date cited complete with day of the week is 6 February AD 60, identified as a "Sunday" (as "eighth day before the ides of February, day of the Sun") in a Pompeiian graffito. According to the (contemporary) Julian calendar, 6 February 60 was, however, a Wednesday. This is explained by the existence of two conventions of naming days of the weeks based on the planetary hours system: 6 February was a "Sunday" based on the sunset naming convention, and a "Wednesday" based on the sunrise naming convention.
Adoption in Asia.
China and Japan.
The earliest known reference in Chinese writings to a seven-day week is attributed to Fan Ning, who lived in the late 4th century in the Jin Dynasty, while diffusions from the Manichaeans are documented with the writings of the Chinese Buddhist monk Yi Jing and the Ceylonese or Central Asian Buddhist monk Bu Kong of the 7th century (Tang Dynasty).
The Chinese variant of the planetary system was brought to Japan by the Japanese monk Kūkai (9th century). Surviving diaries of the Japanese statesman Fujiwara Michinaga show the seven-day system in use in Heian Period Japan as early as 1007. In Japan, the seven-day system was kept in use for astrological purposes until its promotion to a full-fledged Western-style calendrical basis during the Meiji Period (1868–1912).
India.
The seven-day week was known in India by the 6th century, referenced in the Pañcasiddhāntikā. Shashi (2000) mentions the Garga Samhita, which he places in the 1st century BC or AD, as a possible earlier reference to a seven-day week in India. He concludes "the above references furnish a terminus ad quem (viz. 1st century) The terminus a quo cannot be stated with certainty".
Arabia.
In Arabia, a similar seven-day week system was adopted, which may have been influenced by the Hebrew week (via Christianity). 
Christian Europe.
The seven-day weekly cycle has remained unbroken in Christendom, and hence in Western history, for almost two millennia, despite changes to the Coptic, Julian, and Gregorian calendars, demonstrated by the date of Easter Sunday having been traced back through numerous computistic tables to an Ethiopic copy of an early Alexandrian table beginning with the Easter of AD 311.
A tradition of divinations arranged for the days of the week on which certain feast days occur develops in the Early Medieval period. There are many later variants of this, including the German "Bauern-Praktik" and the versions of "Erra Pater" published in 16th to 17th century England, mocked in Samuel Butler's "Hudibras". South and East Slavic versions are known as "koliadniki" (from "koliada", a loan of Latin "calendae"), with Bulgarian copies dating from the 13th century, and Serbian versions from the 14th century.
Medieval Christian traditions associated with the lucky or unlucky nature of certain days of the week survived into the modern period. This concerns primarily Friday, associated with the crucifixion of Jesus. Sunday, sometimes personified as Saint Anastasia, was itself an object of worship in Russia, a practice denounced in a sermon extant in copies going back to the 14th century.
Sunday, in the ecclesiastical numbering system also counted as the "feria prima" or the first day of the week; yet, at the same time, figures as the "eighth day", and has occasionally been so called in Christian liturgy.
Justin Martyr wrote: "the first day after the Sabbath, remaining the first of all the days, is called, however, the eighth, according to the number of all the days of the cycle, and [yet] remains the first."
A period of eight days, usually (but not always, mainly because of Christmas Day) starting and ending on a Sunday, is called an octave, particularly in Roman Catholic liturgy. In German, the phrase "heute in acht Tagen" (literally "today in eight days") means one week from today (i.e. on the same weekday). The same is true of the Italian phrase "oggi otto" (literally "today eight").
Week numbering.
Weeks in a Gregorian calendar year can be numbered for each year. This style of numbering is often used in European and Asian countries. It is less common in the U.S. and elsewhere.
The ISO week date system.
The system for numbering weeks is the ISO week date system, which is included in ISO 8601. This system dictates that each week begins on a Monday and is associated with the year that contains that week's Thursday.
Determining "Week 1".
In practice week 1 ("W01" in ISO notation) of any year can be determined as follows:
Examples:
Week 52 and 53.
It is also possible to determine if the last week of the previous year was Week 52 or Week 53 as follows:
Schematic representation of ISO week date.
! rowspan=2 | Dominical<br>letter(s)1
! colspan=7 | Days at the start of January
! colspan=4 | Effect1,2
! colspan=7 | Days at the end of December1
! 1<br>Mon || 2<br>Tue || 3<br>Wed ||4<br>Thu || 5<br>Fri || 6<br>Sat || 7<br>Sun