Pronunciation of mathematical expressions- _7 e' \: s2 W* ?
The pronunciations of the most common mathematical expressions are given in the list- z& B6 N( o$ I
below. In general, the shortest versions are preferred (unless greater precision is necessary). 0 \7 y0 j9 M4 B% C/ X) F% [3 D' {1. Logic% U9 I9 E4 ~- n1 A4 Q2 e
9 there exists6 D6 |$ d1 O$ H
8 for all 1 e& i3 P4 d& i9 l: J+ vp ) q p implies q / if p, then q" v5 U9 h2 l/ [
p , q p if and only if q /p is equivalent to q / p and q are equivalent* s) k# c9 B1 A5 J4 Q1 W. |* Q+ ~
2. Sets& _. ^; Q u. R: ^
x 2 A x belongs to A / x is an element (or a member) of A 6 H4 o/ i- b1 f% x- u+ Q* n4 Xx =2 A x does not belong to A / x is not an element (or a member) of A 7 \0 m7 G4 x" v- _% W) l7 NA ½ B A is contained in B / A is a subset of B1 {5 p) B0 X4 T: B* S9 J n
A ¾ B A contains B / B is a subset of A ) t6 l. z- g. @A \ B A cap B / A meet B / A intersection B 1 Q& v( B. o3 ^& X9 oA [ B A cup B / A join B / A union B: D- W8 \3 o) e" Y* `% s/ a
A n B A minus B / the di®erence between A and B* M: [! N: r4 p7 B
A £ B A cross B / the cartesian product of A and B 0 }# u$ p& d! n3 i. i5 @ z3. Real numbers , J7 E+ t9 G4 ^. }x + 1 x plus one ' Z0 w# K/ c" J( u6 |. Fx ¡ 1 x minus one % C K1 R# n* K" Lx § 1 x plus or minus one3 n: Y- H6 } @: B- W% w% `% m9 T: v
xy xy / x multiplied by y9 F1 J1 C$ k/ v. k/ O# T p
(x ¡ y)(x + y) x minus y, x plus y % j! n. g$ \: r- L! p2 Bx" ^6 t5 k( T( i* c. d4 Z
y* y( C s n( }9 t+ M- A( w
x over y 4 d4 a5 ?* P# G! {# R7 D# O= the equals sign5 Q Y1 v- O) S* |+ d( O
x = 5 x equals 5 / x is equal to 50 O8 c! C8 i% E ~( d& I
x 6= 5 x (is) not equal to 5 ; K. L' G1 ?4 J* p# F8 C% w1! a- @- W. M" v. `5 i
x ´ y x is equivalent to (or identical with) y% x2 T) U- P& W6 ]! Y
x 6´ y x is not equivalent to (or identical with) y4 F& x& g% ^0 a* M
x > y x is greater than y " H! k8 T* ~. y% c" @; Z9 Ix ¸ y x is greater than or equal to y s w2 M" t5 P: v4 t! l' k' Ex < y x is less than y. x6 a5 [ ?8 d) i
x · y x is less than or equal to y- Q, x3 \% o9 Y2 N5 `* ~: H
0 < x < 1 zero is less than x is less than 1: i& I R! k) d- Z. t, w( z" y$ c
0 · x · 1 zero is less than or equal to x is less than or equal to 1 + Z" B( i! a: p# H5 y5 D; f' sjxj mod x / modulus x . L( r" x) t: P0 t( c9 ]0 _4 f0 w9 ux2 x squared / x (raised) to the power 2- ?7 h: _/ e4 Z
x3 x cubed 2 a0 x2 G) Y4 R ix4 x to the fourth / x to the power four# ?/ w3 V% |0 I
xn x to the nth / x to the power n; a2 x7 C% ^' @5 ^3 x
x¡n x to the (power) minus n4 A1 `! X2 W. a( g6 }* V+ M$ j
px (square) root x / the square root of x1 f) B; j. Q/ k: H5 \, ?" `9 |
p3 x cube root (of) x 9 `) J# `# g4 b; m3 x0 yp4 x fourth root (of) x * J& g! \' |' r7 Dnpx nth root (of) x- N+ A5 i3 R: f# }1 p' [3 ?
(x + y)2 x plus y all squared3 p; [: E# ?9 O" P$ i3 ]2 ]' U
³x! ~& u! Y& _8 h R7 W
y9 K6 @9 |, b9 c6 Z* ~ V, Q
´21 k% D7 P4 X0 O
x over y all squared 9 B- R7 a' u1 H; Y) f0 nn! n factorial ! ~% o- d. B( w* O! v# R @^x x hat $ M3 \9 `- L/ v6 K/ _+ H¹x x bar # N& ^" U' z1 n4 j0 O~x x tilde3 G- t0 p3 v& V+ T' p
xi xi / x subscript i / x su±x i / x sub i * s/ m8 A8 ]" i. XXn - V% h e+ Q' j8 e7 ki=1 ! ]( w1 }8 j. f3 S- iai the sum from i equals one to n ai / the sum as i runs from 1 to n of the ai* h% l0 [2 U1 C( D$ j5 U8 R5 P
4. Linear algebra7 [9 y' ~% d. \) l( l9 x" J0 D- H
kxk the norm (or modulus) of x9 ]- t. Y! v+ C) j
O¡¡!A OA / vector OA / M, b( c. V# t1 S& }5 H9 hOA OA / the length of the segment OA ) R5 i8 n6 _9 Q- Y/ HAT A transpose / the transpose of A ! M8 i1 C: |: _& ]% L8 h$ X; B4 BA¡1 A inverse / the inverse of A " F1 `$ N6 N- p. h- M2* O2 Y; Y' ]* P
5. Functions 4 h% `, Y+ \( ^f(x) fx / f of x / the function f of x5 V# A2 ]4 a' N& D9 y6 N
f : S ! T a function f from S to T; M2 a: I. q0 g' u6 F3 @
x 7! y x maps to y / x is sent (or mapped) to y" m5 K" q; s5 Q8 l( [ F
f0(x) f prime x / f dash x / the (¯rst) derivative of f with respect to x : W5 @6 e; A: X+ G7 xf00(x) f double{prime x / f double{dash x / the second derivative of f with. n3 o" F# b9 U- H! k3 w
respect to x ' V' D& \* @' V. E2 Y* v' Sf000(x) f triple{prime x / f triple{dash x / the third derivative of f with respect6 D* s8 V5 ]0 h& F: W& i
to x % K4 b: Y% F$ q' W' Wf(4)(x) f four x / the fourth derivative of f with respect to x : J' I# W. k3 T@f " H& n# [$ q2 N5 J@x13 @2 e3 h1 S* y. C
the partial (derivative) of f with respect to x11 c+ i+ f; W9 b; r* J
@2f . h w2 s* I# n' e. \- D@x21 3 F/ O. z& x" {: W9 e- Sthe second partial (derivative) of f with respect to x16 e" M7 c; m1 @* O! a* b+ x4 r
Z. Q& G8 r* {1 @# M
1 9 W1 ?" V/ f+ X$ k! n5 y0 & M$ k, U# [+ P6 T( gthe integral from zero to in¯nity B; i( `$ t8 B6 Y+ V
lim & n }% ~; R2 m% v6 i) Ax!0 6 v u3 w9 p5 `6 Y6 jthe limit as x approaches zero7 C8 U9 u# o: \
lim " [* x- ~! W; z) o8 \6 U& ex!+0 : H2 |0 f3 d2 K3 l& b0 \the limit as x approaches zero from above3 i! c# |6 Q; U5 v7 r8 o
lim ; ?4 J( k! F/ x9 Zx!¡0* y/ O) p- t2 B
the limit as x approaches zero from below ' c, J+ g8 x5 ], C8 k/ H2 Sloge y log y to the base e / log to the base e of y / natural log (of) y 3 [9 e- x, f: A4 z% c4 y/ ?" pln y log y to the base e / log to the base e of y / natural log (of) y s* H: Y) q9 b2 N. N' @Individual mathematicians often have their own way of pronouncing mathematical expressions ( o' S$ M& k% Q+ l" \5 gand in many cases there is no generally accepted \correct" pronunciation. 1 M% P4 `6 Z; ^Distinctions made in writing are often not made explicit in speech; thus the sounds fx may1 ^2 g5 G9 a: F% ~3 d9 x
be interpreted as any of: fx, f(x), fx, FX, FX, F¡¡X!. The di®erence is usually made clear 0 @3 @2 _8 t" r [- G2 F) sby the context; it is only when confusion may occur, or where he/she wishes to emphasise0 D2 J8 q3 o" d, w. i* {
the point, that the mathematician will use the longer forms: f multiplied by x, the function , y/ b! d' K9 j& s4 ?f of x, f subscript x, line FX, the length of the segment FX, vector FX.' S7 z4 ?8 _: V+ V8 Q- Y+ M+ I
Similarly, a mathematician is unlikely to make any distinction in speech (except sometimes' T3 w: `/ ?* U
a di®erence in intonation or length of pauses) between pairs such as the following: 2 {& W8 p' S. N. i5 tx + (y + z) and (x + y) + z & r# ]5 V s$ o/ |; {pax + b and pax + b0 Z8 a) X" S8 Q0 t% g' l& n
an ¡ 1 and an¡1 1 |- Y. b9 T7 a7 c6 pThe primary reference has been David Hall with Tim Bowyer, Nucleus, English for Science ( o! n. l% S X) [4 uand Technology, Mathematics, Longman 1980. Glen Anderson and Matti Vuorinen have y" ?6 m0 ], C& E+ Mgiven good comments and supplements.. z) U/ z# i/ l) ^
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