Pronunciation of mathematical expressions 5 c$ G4 P; j# S/ {: MThe pronunciations of the most common mathematical expressions are given in the list" n" I7 n% n0 o- J6 J
below. In general, the shortest versions are preferred (unless greater precision is necessary).; z8 O% o$ h3 P* g6 u( b5 o
1. Logic 7 b% f: h ]+ [, U- r9 there exists* T! X! Z0 b" X5 O; w
8 for all% Q4 I& m& Z; Y$ G: O' |
p ) q p implies q / if p, then q/ t$ U9 `/ h1 F( t
p , q p if and only if q /p is equivalent to q / p and q are equivalent- b5 {% O* W6 ^0 {9 E
2. Sets( Z. [/ E# I1 P! @& j+ X8 @4 `( r
x 2 A x belongs to A / x is an element (or a member) of A ; C! W5 t) w3 N% u. o. R. wx =2 A x does not belong to A / x is not an element (or a member) of A) Z# }4 E1 @& s1 l3 x' Z3 ~& Y
A ½ B A is contained in B / A is a subset of B 4 i3 I7 R8 d/ f' x! kA ¾ B A contains B / B is a subset of A 7 K3 {1 S9 _1 k( F4 L9 \- XA \ B A cap B / A meet B / A intersection B ( w, m+ q! V0 f$ o/ q! hA [ B A cup B / A join B / A union B 4 G" _ {3 ^( WA n B A minus B / the di®erence between A and B6 o& @; @1 p0 R6 U
A £ B A cross B / the cartesian product of A and B( t4 \3 G/ v6 a! i
3. Real numbers ! n" z% V- W- ` d. Z' ex + 1 x plus one + o6 X' i8 i$ j G7 _% n4 ^3 ux ¡ 1 x minus one - B/ `' j6 _' F, Fx § 1 x plus or minus one {, y6 H' P/ I4 X
xy xy / x multiplied by y N2 w2 U+ n8 r* g, L(x ¡ y)(x + y) x minus y, x plus y# q% G0 A) v6 H
x 8 Q5 B% Q! J% C; W! q, ]y1 A: o# A X2 d$ U" d6 R. o
x over y2 l% D) V( Q$ s& W4 o) k
= the equals sign / u7 [ ?: @& Sx = 5 x equals 5 / x is equal to 5 8 s, k7 Z* O" G$ Tx 6= 5 x (is) not equal to 5 + q. b- @+ A' V17 C7 c- R0 S9 S( F# U" m
x ´ y x is equivalent to (or identical with) y$ u$ i# k, G, ^6 n
x 6´ y x is not equivalent to (or identical with) y; }2 u0 @ H1 W I* `
x > y x is greater than y 7 u: w$ ?6 U1 F" w+ Ix ¸ y x is greater than or equal to y + g7 A3 v6 c5 _' H% f7 `5 hx < y x is less than y ' Y2 P2 N: b1 [+ o8 {6 qx · y x is less than or equal to y" J! j7 q$ s, `/ {+ n" b
0 < x < 1 zero is less than x is less than 1 7 q8 h! p# O6 a: i, a# |# K3 p0 · x · 1 zero is less than or equal to x is less than or equal to 1$ b8 e0 p4 M, m$ [, F
jxj mod x / modulus x ! ]" b J, P0 \0 q# cx2 x squared / x (raised) to the power 2 ; x7 K6 d- @& |3 X% F# f) Gx3 x cubed. ^6 |: M% o" G7 E
x4 x to the fourth / x to the power four3 f( |: T; g: ^8 `" V+ H
xn x to the nth / x to the power n 1 \: Y5 k; p6 n' y+ ix¡n x to the (power) minus n3 {0 I) T3 q" o# Z
px (square) root x / the square root of x : z s4 f7 }) v: w6 s, zp3 x cube root (of) x # ^' m; ^$ ^& j# G* h, Up4 x fourth root (of) x" M0 G \; L- `* H
npx nth root (of) x 1 @5 X0 E/ X! r' E+ o7 L; ?(x + y)2 x plus y all squared , ~ I* h, g1 t! T# ?³x7 w0 e0 b, \5 _# [, i
y7 {* F2 i; ~: W0 Q& u* X
´2' _! @0 K; R1 p) S# o0 o: c1 r
x over y all squared1 E- U! W# o; e. @
n! n factorial6 y7 ]+ [, c" s$ i' g/ w
^x x hat0 f; U( ^4 f+ S' c$ q1 U
¹x x bar 9 [6 w+ p; i6 h! @- R. f0 L3 f~x x tilde- r; ?" {9 T' e7 j, r1 T0 E8 a$ `
xi xi / x subscript i / x su±x i / x sub i: x* y# k( B4 @' s% d7 x) V* w/ n
Xn- G) k) }1 p& _+ r: W; e% u
i=14 `, m( B0 _0 M" J% M: m" h- l: m
ai the sum from i equals one to n ai / the sum as i runs from 1 to n of the ai/ p$ g" B6 l* a$ o
4. Linear algebra 2 W5 H3 \5 Z; [kxk the norm (or modulus) of x 9 n9 Q6 B3 Q7 b% w5 w0 d; tO¡¡!A OA / vector OA* T; Y2 P3 J! |
OA OA / the length of the segment OA 8 ?* g5 H( A1 B2 ^1 ?* d2 J9 hAT A transpose / the transpose of A. a R7 u7 F2 M" [$ h( Z
A¡1 A inverse / the inverse of A 1 o3 U9 S) z1 s2 M1 |3 V: F# m N: v5. Functions* ?2 Z2 |2 {& n* K8 {8 A6 `
f(x) fx / f of x / the function f of x 7 d# U, e7 K$ f/ k2 d" M6 ~5 Zf : S ! T a function f from S to T. [8 _6 D, s; @8 n9 k( j ~
x 7! y x maps to y / x is sent (or mapped) to y" t' k4 R& x1 b, v
f0(x) f prime x / f dash x / the (¯rst) derivative of f with respect to x( k1 j! A0 z9 g+ G7 k
f00(x) f double{prime x / f double{dash x / the second derivative of f with7 w0 i) t+ G, v0 t2 X' y, f) L
respect to x 1 k+ v: g6 S, Y: g S7 S: |0 uf000(x) f triple{prime x / f triple{dash x / the third derivative of f with respect1 ]1 H6 ~3 |7 D1 u! w
to x 2 w/ Z- |' ^+ A5 hf(4)(x) f four x / the fourth derivative of f with respect to x6 b# j1 t2 z, e1 I- ]* P( M6 @! q
@f . u1 t @" B$ ~+ k/ b@x1$ \! Q" N `( ?. @3 q3 I, C
the partial (derivative) of f with respect to x14 X# f( o' }! a
@2f% U& E5 I& I) T6 C- _3 J. R
@x21 ; u, J. w8 X5 b; H$ v; t8 m! v5 Athe second partial (derivative) of f with respect to x1; i! J8 r9 z: W
Z 6 X( K6 H; e8 B& {0 N U a1, @) N- ^, H) K2 G: `
05 j( V; w$ u! [4 D8 b6 R
the integral from zero to in¯nity 6 n9 z2 _5 @' @+ Klim * N/ T: M2 Q( m; h3 qx!0$ j, U9 @7 a" W$ K1 h' I# I, f. z9 S
the limit as x approaches zero0 h, L) C0 a/ D E) f3 B+ \# s8 X
lim" d2 ?6 J8 l$ s
x!+0: @1 [! ?/ H' s1 Z
the limit as x approaches zero from above4 c- I( j7 C t6 \
lim4 A( S0 x- i; [1 O' z3 |! g
x!¡0* \; J* ^% F4 y
the limit as x approaches zero from below 2 @$ J& y/ c. d% M2 q5 gloge y log y to the base e / log to the base e of y / natural log (of) y , i. D1 a1 ]$ v) m' Aln y log y to the base e / log to the base e of y / natural log (of) y% J" N7 d2 a& @) }
Individual mathematicians often have their own way of pronouncing mathematical expressions; C, y4 a9 ~# P8 P) q; l, T& r+ v
and in many cases there is no generally accepted \correct" pronunciation. . j! f0 x' R# QDistinctions made in writing are often not made explicit in speech; thus the sounds fx may9 O/ ?! Z/ [3 p4 ~4 `
be interpreted as any of: fx, f(x), fx, FX, FX, F¡¡X!. The di®erence is usually made clear # H3 t( z/ X! z7 x* {4 f" ~& _by the context; it is only when confusion may occur, or where he/she wishes to emphasise + c6 Q7 l& C# Othe point, that the mathematician will use the longer forms: f multiplied by x, the function: X j1 ]' H( `) K. c; u4 f$ Z$ m# n
f of x, f subscript x, line FX, the length of the segment FX, vector FX. 4 j3 T2 L! z/ b" ]! g8 OSimilarly, a mathematician is unlikely to make any distinction in speech (except sometimes! W( b5 X0 e- u
a di®erence in intonation or length of pauses) between pairs such as the following:3 g+ e4 w g9 g& I1 I7 Z8 ?# E
x + (y + z) and (x + y) + z 5 P: W. a/ @, A' vpax + b and pax + b 3 l& ]" `7 e6 qan ¡ 1 and an¡1 ! k# U* E1 r+ `, H$ H: ?; g0 xThe primary reference has been David Hall with Tim Bowyer, Nucleus, English for Science 4 ]2 I' n( q- t7 a N9 f9 Land Technology, Mathematics, Longman 1980. Glen Anderson and Matti Vuorinen have+ a( O0 ~0 V1 F5 f' B* _4 b
given good comments and supplements.' D; W* p7 `. V7 O _: r
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