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Mathematical symbols are used internationally but each country read them in its own way. Moreover it is often difficult to find a comprehensive list.

I know that this question is very broad but I think that it could be useful to a lot of people to know how to read the most often found symbols.

By most general symbols I mean: limits, product/union over sets, integrals, (partial) derivatives, etc.

So this question is really about how to read math aloud. If I need to find the name of a particular notion like "signal processing" I can ask Wikipedia.

Edit: Here is a list of what I would like to see covered in an answer.

  • Fraction: a/b is read "a over b" ;
  • Functions: f(x) is read "f of x" ;
  • Inverse image: f^{-1}(A) is read "the inverse image of A by f" ;
  • Direct image: f(A) is read "the direct image of A by f" ;
  • Powers: a^n is read "a to the n-th" ;
  • Limits: lim_{x -> 0} f(x) = 0 can be read "limit of f of x is 0 when x goes to 0" ;
  • Derivative: "df/dx" is read "the derivative of f with respect to x" ;
  • Integral: "Integrate f from a to b with respect to x" ;
  • Unions and Product of sets ;
  • A ⊂ B is read "A susbset of B" ;
  • a ∈ A is read "a in A" ;
  • quantifiers: forall and exists ;
  • symbols big sum and big product (ie. sum from n equals 0 to n = infinity) ;
  • binomial coefficient ;
  • how the reading of (3 + 2) * 2 differs from 3 + 2*2 ;
  • how to read the for basic operations +,×,÷,- in context ;
  • P(X|Y) is read "probability of X given Y" ;
  • P(X = k) is read "probability that X becomes k" ;
  • Square roots, n-th roots ;
  • Elementary functions : exp, log, log_a, cos, sin, tan, cosh, sinh, tanh and their inverse.

I tried to be comprehensive on symbols you may find very often. If you think that I forget some very important symbols please notify me.

  • 1
    As you say, this question might be a little broad as there are a lot of mathematical symbols! Maybe you could ask about some common ones, and then ask about any other specific ones in separate questions? – topo Reinstate Monica Jun 23 '16 at 7:58
  • 1
    @topomorto Then I will include a minimum requirements list for what I expect to be common symbols. – Lyle Jun 23 '16 at 8:06
  • Partial answer: A ⊂ B is read "A는 B의 부분집합". For other notations, I have to read my math textbooks... – choco_addicted Jun 23 '16 at 8:29
  • I'd like to add (square) root (√) and (natural) logarithm (ln, log). – 파울울 Jun 23 '16 at 10:52
  • There was a great list on Reddit. reddit.com/r/Korean/comments/40qise/how_do_i_read_math_problems/… Can we recycle that answer here? – 파울울 Jun 23 '16 at 10:54
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Reddit user /u/skyhi14 has written up a very good post on this fairly recently. Here's a link to his original post.

Arithmetic

  • + − × ÷ = : 더하기, 빼기, 곱하기, 나누기, 은/는 respectively
  • Decimal point : 점
  • Parenthesis : 괄호 열고 / 괄호 닫고
  • ± : 플러스마이너스
  • +a, -a : 플러스 a, 마이너스 a

    48÷2(9+3) → 사십팔 나누기 이 괄호 열고 구 더하기 삼 괄호 닫고

Fraction

  • a / b : b 분의 a

Powers and nth root

  • n^2 : n의 제곱
  • n^k : n의 k승 / n의 k제곱

    2^8 → 이의 팔승
    a^(1/8) → a의 팔분의 일승

  • Square root : 루트
  • Cubic root : 삼 승 루트

    -b ±√(b^2 − 4ac) / 2a → 이 에이 분의 마이너스 비 플러스마이너스 루트 비 제곱 마이너스 사 에이시

Factorial

  • a! : a 팩토리얼

Logarithm

  • log_a(x) : 로그 a x
  • log(x) : 로그 x
  • ln(x) : 자연로그 x / 엘엔 x

Limit

  • lim(a→x) expr : 리미트 a가 x로 갈 때 expr
  • lim(a→∞) expr : 리미트 a가 무한대로 갈 때 expr

Summation

  • Σ (k=m→n) ak : 시그마 k는 m에서 n까지일 때 ak

Function

  • f(x) : f x (에프 엑스)

Trigonometric function

  • sin(x) : 사인 x
  • cos, tan : 코사인, 탄젠트
  • cosec/csc, sec, cot : 코시컨트, 시컨트, 코탄젠트
  • asin, acos, atan, … : 아크사인, 아크코사인, 아크탄젠트

Integral

  • ∫ f(x)dx : 인테그럴 f x dx(에프 엑스 디엑스)
  • ∫[a,b] f(x)dx : 인테그럴 a에서 b까지 f x dx(에프 엑스 디엑스)

Symbols

  • ∞ : 무한대
  • ʹ : 프라임
  • ^— : 바
  • 2
    This answer is already good but it covers things I forgot to add to my list but also, it omits things in my list. So I may suggest that we reassemble every thing in a community wiki answer. What do you think about it? – Lyle Jun 24 '16 at 10:22
  • @永劫回帰 Great idea. I'll convert it to a community wiki. – user12 Jun 25 '16 at 16:47
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Wow, it's a lot. I will answer some and I hope others will answer more!

Fraction: a/b is read "a over b" -> b분의 a (yes, the order is reversed!)

Functions: f(x) is read "f of x" -> 에프 엑스 (just f(x) read in Korean)

Powers: a^n is read "a to the n-th" -> a의 n제곱

+-*/: + -> 더하기, - -> 빼기, * -> 곱하기, / -> 나누기

+-*/ are always 더하기, 빼기, 곱하기, 나누기. They are not changed like 'multiplication' and 'times' in English, for example.

  • 1
    Some people say f(x) as "에프 오브 엑스". – choco_addicted Jun 23 '16 at 9:47
  • I am not so surprised for the inversion of a and b for fraction (I included it because I suspected it would be so). Just another side question: do you also write the denominator before the numerator (writing fraction up to bottom)? – Lyle Jun 23 '16 at 9:59
  • No. When the fractions are written, the denominators are in the right side or lower side as usual. For example, "7분의 4" is 4/7. – JSong Jun 23 '16 at 10:07
  • Yes, I may not have been clear. When you write (on paper) 4/7, do you write first 4 or 7? – Lyle Jun 23 '16 at 10:20
  • @永劫回帰 Oh I see! For me, I usually write from bottom to top. So I write 7 first, horizontal bar next, and 4 last. – JSong Jun 24 '16 at 1:44
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P(X|Y) : 사건Y가 일어났을 때의 사건 X의 조건부확률

또는 사건 Y에 대한 사건 X의 조건부 확률

또는 사건 Y가 일어났을때 사건 X가 일어날 확률

P(X=k) : X가 k일 확률

f:X -> Y : X를 f의 정의역, Y를 f의 공역. f(X)는 f의 치역

f^{-1}(A) : f에 의한 A의 역상

sinh : 쌍곡사인(hyperbolic sine) 또는 하이퍼 사인

df/dx : f의 x에서의 미분

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