A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various types, many symbols are needed for expressing all mathematics.

The most basic symbols are the decimal digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9), and the letters of the Latin alphabet. The decimal digits are used for representing numbers through the Hindu–Arabic numeral system. Historically, upper-case letters were used for representing points in geometry, and lower-case letters were used for variables and constants. Letters are used for representing many other sorts of mathematical objects. As the number of these sorts has remarkably increased in modern mathematics, the Greek alphabet and some Hebrew letters are also used. In mathematical formulas, the standard typeface is italic type for Latin letters and lower-case Greek letters, and upright type for upper case Greek letters. For having more symbols, other typefaces are also used, mainly boldface , script typeface  (the lower-case script face is rarely used because of the possible confusion with the standard face), German fraktur , and blackboard bold  (the other letters are rarely used in this face, or their use is unconventional).

The use of Latin and Greek letters as symbols for denoting mathematical objects is not described in this article. For such uses, see Variable (mathematics) and List of mathematical constants. However, some symbols that are described here have the same shape as the letter from which they are derived, such as  and .

These letters alone are not sufficient for the needs of mathematicians, and many other symbols are used. Some take their origin in punctuation marks and diacritics traditionally used in typography; others by deforming letter forms, as in the cases of  and . Others, such as  and , were specially designed for mathematics.

Layout of this article
Normally, entries of a glossary are structured by topics and sorted alphabetically. This is not possible here, as there is no natural order on symbols, and many symbols are used in different parts of mathematics with different meanings, often completely unrelated. Therefore, some arbitrary choices had to be made, which are summarized below.

The article is split into sections that are sorted by an increasing level of technicality. That is, the first sections contain the symbols that are encountered in most mathematical texts, and that are supposed to be known even by beginners. On the other hand, the last sections contain symbols that are specific to some area of mathematics and are ignored outside these areas. However, the long section on brackets has been placed near to the end, although most of its entries are elementary: this makes it easier to search for a symbol entry by scrolling.

Most symbols have multiple meanings that are generally distinguished either by the area of mathematics where they are used or by their syntax, that is, by their position inside a formula and the nature of the other parts of the formula that are close to them.

As readers may not be aware of the area of mathematics to which is related the symbol that they are looking for, the different meanings of a symbol are grouped in the section corresponding to their most common meaning.

When the meaning depends on the syntax, a symbol may have different entries depending on the syntax. For summarizing the syntax in the entry name, the symbol  is used for representing the neighboring parts of a formula that contains the symbol. See  for examples of use.

Most symbols have two printed versions. They can be displayed as Unicode characters, or in LaTeX format. With the Unicode version, using search engines and copy-pasting are easier. On the other hand, the LaTeX rendering is often much better (more aesthetic), and is generally considered a standard in mathematics. Therefore, in this article, the Unicode version of the symbols is used (when possible) for labelling their entry, and the LaTeX version is used in their description. So, for finding how to type a symbol in LaTeX, it suffices to look at the source of the article.

For most symbols, the entry name is the corresponding Unicode symbol. So, for searching the entry of a symbol, it suffices to type or copy the Unicode symbol into the search textbox. Similarly, when possible, the entry name of a symbol is also an anchor, which allows linking easily from another Wikipedia article. When an entry name contains special characters such as [, ], and |, there is also an anchor, but one has to look at the article source to know it.

Finally, when there is an article on the symbol itself (not its mathematical meaning), it is linked to in the entry name.

Arithmetic operators

Equality, equivalence and similarity

Comparison

Set theory

Basic logic 
Several logical symbols are widely used in all mathematics, and are listed here. For symbols that are used only in mathematical logic, or are rarely used, see List of logic symbols.

Blackboard bold

The blackboard bold typeface is widely used for denoting the basic number systems. These systems are often also denoted by the corresponding uppercase bold letter. A clear advantage of blackboard bold is that these symbols cannot be confused with anything else. This allows using them in any area of mathematics, without having to recall their definition. For example, if one encounters  in combinatorics, one should immediately know that this denotes the real numbers, although combinatorics does not study the real numbers (but it uses them for many proofs).

Calculus

 

(Capital Greek letter delta—not to be confused with , which may denote a geometric triangle or, alternatively, the symmetric difference of two sets.}}

(Note: the notation  is not recommended for the four-gradient since both  and  are used to denote the d'Alembertian; see below.)

 (here an actual box, not a placeholder)

Linear and multilinear algebra

Advanced group theory

Infinite numbers

Brackets
Many sorts of brackets are used in mathematics. Their meanings depend not only on their shapes, but also on the nature and the arrangement of what is delimited by them, and sometimes what appears between or before them. For this reason, in the entry titles, the symbol  is used as a placeholder for schematizing the syntax that underlies the meaning.

Parentheses

Square brackets

Braces

Other brackets

Symbols that do not belong to formulas
In this section, the symbols that are listed are used as some sorts of punctuation marks in mathematical reasoning, or as abbreviations of natural language phrases. They are generally not used inside a formula. Some were used in classical logic for indicating the logical dependence between sentences written in plain language. Except for the first two, they are normally not used in printed mathematical texts since, for readability, it is generally recommended to have at least one word between two formulas. However, they are still used on a black board for indicating relationships between formulas.

Miscellaneous

See also

Related articles 
 Language of mathematics
 Mathematical notation
 Notation in probability and statistics
 Physical constants

Related lists 
 List of mathematical symbols by subject
 List of logic symbols
 List of mathematical constants
 Table of mathematical symbols by introduction date
 Blackboard bold
 Greek letters used in mathematics, science, and engineering
 List of mathematical uses of Latin letters
 List of common physics notations
 List of letters used in mathematics and science
 List of mathematical abbreviations
 List of typographical symbols and punctuation marks
 ISO 31-11 (Mathematical signs and symbols for use in physical sciences and technology)
 List of APL functions

Unicode symbols 
 Unicode block
 Mathematical Alphanumeric Symbols (Unicode block)
 List of Unicode characters
 Letterlike Symbols
 Mathematical operators and symbols in Unicode 
 Miscellaneous Mathematical Symbols: A, B, Technical
 Arrow (symbol) and Miscellaneous Symbols and Arrows
 Number Forms
 Geometric Shapes

References

External links
 Jeff Miller: Earliest Uses of Various Mathematical Symbols
 Numericana: Scientific Symbols and Icons
 GIF and PNG Images for Math Symbols
 Mathematical Symbols in Unicode
 Detexify: LaTeX Handwriting Recognition Tool

 Some Unicode charts of mathematical operators and symbols:
 Index of Unicode symbols
 Range 2100–214F: Unicode Letterlike Symbols
 Range 2190–21FF: Unicode Arrows
 Range 2200–22FF: Unicode Mathematical Operators
 Range 27C0–27EF: Unicode Miscellaneous Mathematical Symbols–A
 Range 2980–29FF: Unicode Miscellaneous Mathematical Symbols–B
 Range 2A00–2AFF: Unicode Supplementary Mathematical Operators

 Some Unicode cross-references:
 Short list of commonly used LaTeX symbols and Comprehensive LaTeX Symbol List
 MathML Characters - sorts out Unicode, HTML and MathML/TeX names on one page
 Unicode values and MathML names
 Unicode values and Postscript names from the source code for Ghostscript

 

Mathematics
Symbols
Symbols
Symbols
Wikipedia glossaries using description lists
수학 기호(數學記號)는 수학에서 쓰는 기호이며 수, 계산, 논리 등 수학의 개념을 간결하게 표현하기 위해 사용한다. 흔히 사용하는 기호로 사칙연산의 + (더하기표), − (빼기표), × (곱하기표), ÷ (나누기표) 등이 있다. 또한 많은 수학 기호의 이름은 유명한 수학자들의 업적을 기리기 위해 그들의 이름을 차용하여 짓기도 한다.

복잡한 수식에서는 기호의 남용이 발생할 수도 있다.

기본 기호

등호, 디비전 기호

방향 지시 기호

라틴 문자 기반 기호

비문자 기호

순환기호 
≠0 <|> 1/|y|≠0, 0+x≠0 <|> 0-x≠0, x+y≠0 <|> -x-y≠0, x-3≠0 <|> -x+3≠0x ≠3, x+y=z <|> -x-y=z  역 ≠0이 아니고, 기호들을 역했을때

A⇔B≠0<|>B⇔A≠0(4차원)는 A⇔B이고, B⇔A이면, 기호들의 역이다.

목록

연산(관계연산) 

  등호
  부등호
  
 부등식
  (해석적 수론) 많은 차이에서 크거나, 작다 또는 산술 시프트 연산자
  크거나 같다, 작거나 같다
  Karp 감소
   유사 관계 기호
  덧셈
  뺄셈
   곱셈
   곱셈
  곱셈
  나눗셈
  덧셈 또는 뺄셈
  뺄셈 또는 덧셈

연산자(기능연산)  
  팩토리얼(계승)   준계승(sub factorial)
 또는  빅 오(Big O), 리틀 오(little o), 점근 표기법 
  루트
  급수, 수열의 합
  곱집합, 데카르트 곱, 곱연산
  쌍대곱
  미분, 도함수
   곱셈, 스칼라 곱,  점곱, 그리고(and)
  적분
또는  적분 연산 (치환적분)
  폐곡선관련 적분
  발산 또는 함수의 기울기 또는 델 (연산자) 또는 나블라
  편미분
  미분,도함수 또는 참고- 판별식
  크로네커 델타,텐서
  약수 함수
  베르누이 수 또는 벨 수
  오일러 수
  함수의 극한, 수열의 극한
  subtype 상,하위 관계, 포함관계
 cover 상,하위 관계, 포함관계
  켤레전치 또는 소멸자 및 생성자 관련(Creation and annihilation operators)
  텐서 곱(tensor product)
 달랑베르시안 연산자
  라플라스 연산자, 미분 연산자, 유한차분연산자
  디랙 연산자
 커누스 윗화살표 표기법 연산자
 최대공약수(Greatest Common Divisor)
 최소공배수(Least Common Multiple)
 켤레복소수
 추정량, 단위벡터
또는 산술 기하 평균
 거리 공간의 지름
 거리 공간의 길이
 지수 적분 함수
 로그 적분 함수
 유수
 클레이니 스타 또는 복소켤레 또는 가역원군
또는  집합의 합집합, 집합연산
 합성곱 
 포흐하머 기호(상승 팩토리얼, 하강 팩토리얼)
 순환소수
 쌍곡 사인

논리 

 

 아니다 (부정)
  아니다 (부정) 또는 동치관계 또는 유사 관계 기호
  근사치 유사 관계 기호, 인접 기호
  화환곱
  (군론)정규 부분군,(환론)아이디얼
  (군론)반직접곱
관계대수
  따라서, 그러므로
  왜냐하면
  QED - "증명 끝" 또는 조건 명제
 
 이다 , 함의
   동치
  그리고
   또는
 직합
   모든, 임의의,전칭기호
   존재한다
  유일하다
  정의하다, 참조-논리 기호
  한정 합동
  합동, 합동 산술
  항진, 언제나 참이다
  참이다,  참조-논리 기호
  모순,  참조-논리 기호
  명제 논리,  참조-논리 기호
 명제 논리,  참조-논리 기호
  노름(norm), 최접근 정수함수(Nearest integer function)
  약수이다
 약수가 아니다
  합, 불 논리
  곱, 불 논리 
 예를 들면(발음: for example)
 즉 (발음: namely)
 바꾸어 말하면(발음: that is 또는 [áiìː])

집합 
  원소나열법
 조건제시법
  공집합
 포함관계기호,원소기호
 포함관계기호
 부분집합
 진부분집합
 부분집합
 진부분집합
  합집합
  교집합
  여집합
 여집합 또는 프랙털
  이다
  함수의 합성, 합성함수 기호  써클
  집합의 크기(cardinality) 또는 농도(濃度), 기수
  알레프 수, 가산집합의 농도
  베트 수
 사상의 표기
 사상의 표기
 또는   상한 
 또는  하한
 최대 원소, 최소 원소
  곱집합
또는  집합의 합집합
 전단사함수
 A에 대하여 멱집합

수 
  자연수의 집합
  소수
 
 정수
 (합동 산술)정수환 가환환
  p진 정수환

  유리수
  실수
  복소수
  복소수의 실수부
  복소수의 허수부
  헤이팅 대수(Heyting algebra)

상수 
  무한,인피니티
  파이
  켤레복소수, 농도(card)
  허수,아이(i) 
  e(이)
  지수 함수, 지수
  지수,파우워(nth power)

   2의 제곱근
 기타 여러 수학 상수 들

괄호 
  절대값, 행렬식, 노름(norm)
 바닥함수 
 천장함수 
 최접근 정수함수(Nearest integer function)
  행렬식, 최접근 정수함수(Nearest integer function)
   행렬, 바닥함수(가우스 기호)
   폐구간 
  튜플, 행렬식
 우선 연산 기호 또는 행렬 또는 행렬식 또는 조합
 축 좌표계, 튜플
   개구간 
    반개(폐)구간
    반개(폐)구간
 순서쌍, 튜플
 브라-켓 표기법
브라-켓 표기법#선형연산자와 브라-켓 선형연산자
 내적
 브라-켓 표기법 ket
 브라-켓 표기법 bra
큐-아날로그(큐-브라켓)
또는  포흐하머 기호
큐-포흐하머 기호(q-Pochhammer symbol) 또는 큐-쉬프티드 팩토리얼(q-shifted factorial)
 오일러 수

행렬
 고전적 수반행렬
 전치행렬
 행렬식
 단위행렬
 대각행렬
 역행렬
 켤레전치행렬
 대각합

같이 보기 
 위키백과:TeX 문법(수학 기호)
 :분류:인쇄 약물
 수학 상수
 기호의 남용

각주