Pronunciation of mathematical expressions , V) N, L) {4 {# G+ V0 lThe pronunciations of the most common mathematical expressions are given in the list ) D( J8 Z9 \7 [+ V$ @; mbelow. In general, the shortest versions are preferred (unless greater precision is necessary).- `2 ], M9 _7 O9 E
1. Logic B7 N" H- t! N) {" U2 V* D9 there exists : Y! z9 d9 Q; L" ?7 z1 [8 for all9 R1 q5 p: P9 Z. l* u# D1 J; u
p ) q p implies q / if p, then q E7 T; ~# _1 n3 Y/ w( I/ @p , q p if and only if q /p is equivalent to q / p and q are equivalent . N9 E9 {. z. c1 a0 N& l* }2. Sets8 _( F! f/ P9 y2 z/ u$ y( i
x 2 A x belongs to A / x is an element (or a member) of A3 ]0 O3 k9 t- Z: {: x
x =2 A x does not belong to A / x is not an element (or a member) of A; ?8 J+ c" D7 l" L. {
A ½ B A is contained in B / A is a subset of B( B: T# A5 W( k
A ¾ B A contains B / B is a subset of A+ n: V# O) ^+ Q
A \ B A cap B / A meet B / A intersection B* \8 {- | T5 ^1 w
A [ B A cup B / A join B / A union B 2 V. U6 G, G( ?( lA n B A minus B / the di®erence between A and B 5 e- F! i- F3 j& mA £ B A cross B / the cartesian product of A and B2 |$ I* m" s+ T/ Z2 w. d% P* L# a- F$ M
3. Real numbers 8 E+ j: t2 r+ jx + 1 x plus one( L1 q- u1 G% u5 P! K, s( u. _6 t
x ¡ 1 x minus one1 \9 K+ K. x+ F& e1 Y
x § 1 x plus or minus one( u2 g, @2 x) U# p
xy xy / x multiplied by y 5 \9 w$ ^. \( z$ y' \(x ¡ y)(x + y) x minus y, x plus y : X' o% E% O; {2 v; Qx % @$ X$ }2 q# K4 f* R. t" }+ v/ ey. J; k% o% D! g" x! k7 m8 n
x over y1 t3 C8 x5 O4 r$ }- O; d* F; ?
= the equals sign 0 V; A' t4 s* v- X% sx = 5 x equals 5 / x is equal to 58 V0 X$ q$ p7 j2 |1 ^
x 6= 5 x (is) not equal to 5 + G1 l4 t6 ?6 T& A# f1 ( q! A! k m% A0 y, Z. F, cx ´ y x is equivalent to (or identical with) y& ^3 S+ m- p3 ^9 k" s4 o
x 6´ y x is not equivalent to (or identical with) y 4 J8 N: x& L5 M2 A! kx > y x is greater than y ( ~( o9 p7 \0 d2 T6 rx ¸ y x is greater than or equal to y% f! F8 Z+ Q Y$ i
x < y x is less than y$ n1 o- ^& k/ Q% V2 g, T
x · y x is less than or equal to y f# h1 V8 p( q& J" X2 C8 v1 R' Q& t/ W
0 < x < 1 zero is less than x is less than 1 2 u$ {3 z. b5 V2 x. k& Z0 · x · 1 zero is less than or equal to x is less than or equal to 1 3 d" N6 Q0 X+ f8 \& Cjxj mod x / modulus x ; r3 \' ~6 b2 C) j1 C8 Fx2 x squared / x (raised) to the power 2 9 a9 A; a0 G: R# _9 j px3 x cubed ( L q( ]" E, U6 m! Tx4 x to the fourth / x to the power four 3 w( D: S# A( Q; t/ Ixn x to the nth / x to the power n ( Q, v& \3 q1 F Z4 H9 v n5 Ux¡n x to the (power) minus n& _0 v9 G$ G) i8 H' ^& G! g0 N
px (square) root x / the square root of x: b( v$ J, k5 V( S2 z5 Q
p3 x cube root (of) x3 w9 A, l, P* ]6 Q' K" N# S3 A, m
p4 x fourth root (of) x 0 u$ K# h, z1 A8 O. ^+ @) J9 Wnpx nth root (of) x' w5 }* `9 Q M9 t9 [' w
(x + y)2 x plus y all squared* M" F% S% h7 E- Z. R9 X; @7 |+ C
³x 5 r7 Y0 Z5 i7 {1 I) @5 H( ^y" P5 T, }9 a3 F) F4 a. a# f" `* B& j; I
´2 % l, ~3 @% _3 |/ P+ d3 N) Z+ ^x over y all squared % T( F, a* m$ B* G0 H! S4 Gn! n factorial $ l6 R/ j7 B e8 g4 G^x x hat # ^, a1 }# }+ F- f1 T- R/ c! c5 S¹x x bar ! N. D* x2 ]% ]% N/ R- o+ p~x x tilde , [+ S9 `$ A z% z) h zxi xi / x subscript i / x su±x i / x sub i / u0 L+ Z( I$ o# WXn$ @; a* Y c- O: G% V
i=1 3 L1 z/ V4 Q S5 zai the sum from i equals one to n ai / the sum as i runs from 1 to n of the ai; L' D* t) `* p9 y% y) j
4. Linear algebra$ e" s: z. p1 \- I F- f" v
kxk the norm (or modulus) of x# R1 g% K; ^5 Z( P, R
O¡¡!A OA / vector OA ) T2 h- g: b9 o; S% U% d/ D& gOA OA / the length of the segment OA4 [! e6 p1 n: O. u' A; N+ P8 X
AT A transpose / the transpose of A; Q7 F; H+ ~4 m1 D4 ~
A¡1 A inverse / the inverse of A5 w6 {' h8 M9 f3 \9 M' n6 r( T* V
2* N* P8 {. R% i$ w$ o1 H% a
5. Functions9 n; X! J' v. R2 R- P( [$ A+ \
f(x) fx / f of x / the function f of x0 P( B9 ^( h0 S, y+ x5 `
f : S ! T a function f from S to T6 \- }) Y1 a' s" o- M, ?1 a* Q
x 7! y x maps to y / x is sent (or mapped) to y/ {" }5 \( w7 A" M. k# I7 }
f0(x) f prime x / f dash x / the (¯rst) derivative of f with respect to x! F' X7 ~1 K d2 T# A
f00(x) f double{prime x / f double{dash x / the second derivative of f with$ M4 E, I% t$ w$ ?
respect to x , ?; }% k- A4 A! R* }! jf000(x) f triple{prime x / f triple{dash x / the third derivative of f with respect) w$ h" z( U: b: Z; F
to x6 X: n$ u8 f; U. m9 a# e
f(4)(x) f four x / the fourth derivative of f with respect to x - R4 q" S3 y. R0 C$ ?2 K9 T@f : }5 V( _2 a. Z@x1 . F9 r o! \0 N: x, _) k) a2 h/ kthe partial (derivative) of f with respect to x1+ y$ b" r& E C) \' U, r0 _+ A
@2f u3 y# b/ N u) w. H
@x21% l# f% l' o& o" I3 }1 h
the second partial (derivative) of f with respect to x1! ]5 H G+ v- ~) q, v& k
Z# o9 W4 G4 R) R3 ?& l
1 4 h9 ~* E+ X5 h# U0 ' }9 `. G& ~% M/ n) @9 Ythe integral from zero to in¯nity 1 p/ f1 N7 k( E8 A/ f/ C5 r# olim6 P* E& h+ D" z! ~
x!0$ w/ a! |9 K8 r
the limit as x approaches zero- P7 H! R: O# p( R( i
lim " I3 F" ?! w/ T- u6 hx!+0 6 E$ j7 M5 Q- p; ]+ h) _5 p* N$ pthe limit as x approaches zero from above 8 \1 o+ l1 \9 k" Slim ! O$ U# u# c N9 _6 Y/ _8 H& X& y, jx!¡0% U) ?0 k" B2 Z s. D/ T
the limit as x approaches zero from below) [6 ]! B' e4 N; x, _% i
loge y log y to the base e / log to the base e of y / natural log (of) y- n z, B: W) ?5 V8 e, J' { D
ln y log y to the base e / log to the base e of y / natural log (of) y% \, u0 E/ D/ k/ x* X; X
Individual mathematicians often have their own way of pronouncing mathematical expressions $ U4 e8 z3 Z; X- h; x6 Oand in many cases there is no generally accepted \correct" pronunciation. 4 s$ |" m( R4 }7 _- t9 cDistinctions made in writing are often not made explicit in speech; thus the sounds fx may * T: T! s5 m3 s, R) G+ h7 ube interpreted as any of: fx, f(x), fx, FX, FX, F¡¡X!. The di®erence is usually made clear5 i. J0 r) V7 M7 p8 P6 [
by the context; it is only when confusion may occur, or where he/she wishes to emphasise' @3 t1 d6 Q" @; K
the point, that the mathematician will use the longer forms: f multiplied by x, the function 8 z- e' L8 ?2 `) {f of x, f subscript x, line FX, the length of the segment FX, vector FX.3 ^. Y# {2 D/ x3 i0 J+ v* z# I1 p( w
Similarly, a mathematician is unlikely to make any distinction in speech (except sometimes 6 L" C" U. U$ ta di®erence in intonation or length of pauses) between pairs such as the following:% K j. J& b4 v- c; I5 x9 o; z6 P
x + (y + z) and (x + y) + z* k: U, L/ h6 p* m0 Q, N" M/ r
pax + b and pax + b) o# h2 j+ v" m4 q' A7 Y
an ¡ 1 and an¡1 + i. n% Z; a F4 {- W. eThe primary reference has been David Hall with Tim Bowyer, Nucleus, English for Science3 g/ t$ B8 _$ k1 Y: E/ o
and Technology, Mathematics, Longman 1980. Glen Anderson and Matti Vuorinen have/ ~; s% f& g% {# q
given good comments and supplements.' e- B& U& l5 A1 P4 P6 t# T# T
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