+plus加号；正号-minus减号；负号±plus or minus正负号×is multiplied by乘号÷is divided by除号＝is equal to等于号≠is not equal to不等于号≡is equivalent to全等于号≌is equal to or approximately equal to等于或约等于号≈is approximately equal to约等于号＜is less than小于号＞is more than大于号is not less than不小于号is not more than不大于号≤is less than or equal to小于或等于号≥is more than or equal to大于或等于号%per cent百分之…‰per mill千分之…∞infinity无限大号∝varies as与…成比例√(square) root平方根∵since; because因为∴hence所以∷equals, as (proportion)等于，成比例∠angle角⌒semicircle半圆⊙circle圆○circumference圆周πpi 圆周率△triangle三角形⊥perpendicular to垂直于∪union of并，合集∩intersection of 交，通集∫the integral of …的积分∑(sigma) summation of总和°degree度′minute分″second秒℃Celsius system摄氏度{open brace, open curly左花括号}close brace, close curly右花括号(open parenthesis, open paren左圆括号)close parenthesis, close paren右圆括号() brackets/ parentheses括号[open bracket 左方括号]close bracket 右方括号[] square brackets方括号.period, dot句号，点|vertical bar, vertical virgule竖线& amp;ampersand, and, reference, ref和，引用*asterisk, multiply, star, pointer星号，乘号，星，指针/slash, divide, oblique 斜线，斜杠，除号//slash-slash, comment 双斜线，注释符#pound井号\backslash, sometimes escape反斜线转义符，有时表示转义符或续行符~tilde波浪符.full stop句号,comma逗号:colon冒号;semicolon分号question mark问号!exclamation mark (英式英语) exclamation point (美式英语)'apostrophe撇号-hyphen连字号-- dash 破折号...dots/ ellipsis省略号"single quotation marks 单引号""double quotation marks 双引号‖ parallel 双线号～swung dash 代字号§section; division 分节号→arrow 箭号；参见号1. Logic9 there exists8 for allp ) q p implies q / if p, then qp , q p if and only if q /p is equivalent to q / p and q are equivalent2. Setsx 2 A x belongs to A / x is an element (or a member) of Ax =2 A x does not belong to A / x is not an element (or a member) of AA ?B A is contained in B / A is a subset of BA ?B A contains B / B is a subset of AA \B A cap B / A meet B / A intersection BA [B A cup B / A join B / A union BA nB A minus B / the di?rence between A and BA ?B A cross B / the cartesian product of A and B3. Real numbersx + 1 x plus onex ?1 x minus onex ?1 x plus or minus onexy xy / x multiplied by y(x ?y)(x + y) x minus y, x plus yxyx over y= the equals signx = 5 x equals 5 / x is equal to 5x 6= 5 x (is) not equal to 51x ?y x is equivalent to (or identical with) yx 6?y x is not equivalent to (or identical with) yx > y x is greater than yx >=y x is greater than or equal to yx < y x is less than yx <=y x is less than or equal to y0 < x < 1 zero is less than x is less than 10 ?x ?1 zero is less than or equal to x is less than or equal to 1jxj mod x / modulus xx^2 x squared / x (raised) to the power 2x^3 x cubedx^4 x to the fourth / x to the power fourx^n x to the nth / x to the power nx☆x to the (power) minus npx (square) root x / the square root of x3 px cube root (of) x4 px fourth root (of) xnpx nth root (of) x(x + y)2 x plus y all squared厨y ?x over y all squaredn! n factorial^x x hat锅x bar~x x tildexi xi / x subscript i / x su兵i / x sub in Xi=1ai the sum from i equals one to n ai / the sum as i runs from 1 to n of the ai 4. Linear algebrakxk the norm (or modulus) of x! OA OA / vector OAOA OA / the length of the segment OAAT A transpose / the transpose of AA? A inverse / the inverse of A25. Functionsf(x) fx / f of x / the function f of xf : S ! T a function f from S to Tx 7! y x maps to y / x is sent (or mapped) to yf0(x) f prime x / f dash x / the (?st) derivative of f with respect to xf00(x) f double{prime x / f double{dash x / the second derivative of f withrespect to xf000(x) f triple{prime x / f triple{dash x / the third derivative of f with respectto xf(4)(x) f four x / the fourth derivative of f with respect to x@f@x1the partial (derivative) of f with respect to x1@2f@x21the second partial (derivative) of f with respect to x1Z 1the integral from zero to in?itylimx!0the limit as x approaches zerolimx!+0the limit as x approaches zero from abovelimx!?the limit as x approaches zero from belowloge y log y to the base e / log to the base e of y / natural log (of) yln y log y to the base e / log to the base e of y / natural log (of) yIndividual mathematicians often have their own way of pronouncing mathematical expressions and in many cases there is no generally accepted \correct" pronunciation.Distinctions made in writing are often not made explicit in speech; thus the sounds fx maybe interpreted as any of: fx, f(x), fx, FX, FX, ! FX . The di?rence is usually made clearby the context; it is only when confusion may occur, or where he/she wishes to emphasisethe point, that the mathematician will use the longer forms: f multiplied by x, the functionf of x, f subscript x, line FX, the length of the segment FX, vector FX.Similarly, a mathematician is unlikely to make any distinction in speech (except sometimesa di?rence in intonation or length of pauses) between pairs such as the following: x + (y + z) and (x + y) + zpax + b and pax + ban ?1 and an?。