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数学专业英语-Notations and Abbreviations (I) Learn to understand
7 B5 v. [& T+ {; i ) A3 s- z+ n. ^: O- t
2 A( _! h/ W7 U $ _" K. y) l/ [8 y! y; A+ b( X
, f+ H9 E+ i' W' G0 w V' ~. b; LN set of natural numbers
' x7 Y) E+ D0 Z [. V( S
/ [) n; D* x9 p9 Z; L/ c; P3 [2 q5 \7 Q. a2 `5 l4 R. `
8 Z8 ~: o5 S* e7 \. q$ P0 p
Z set of integers
0 t: h' g: a" ?0 X4 U+ @$ ~! x9 p' Q1 l8 \8 [6 s1 L5 ?- a4 j
& U% u' r3 v5 Q, { R set of real numbers
" F( j- D* T+ P5 v! k
( P, O. M, W% P0 ]: s
$ k% y6 X& @2 F' q% c& L C set of complex numbers + J. \3 j* n2 F* j
: ~: l+ P6 L, K: O7 C( y0 c
+ q4 q3 M6 e' t, k2 R4 G; D + plus; positive , G+ Y0 r+ [0 j ], [
. i8 S# y, x( h& g& I+ U9 H4 T7 @) m & s4 N1 B( V8 S2 Z* j% ]5 ~
- minus; negative
6 K# U. O0 Y; A8 Z
" [( m+ z# v" h7 u2 N
q/ R0 v" e; h3 S5 B × multiplied by; times
+ u+ s- ]& ~) Y. ^
, v3 U0 A- Z* l' p2 N& p; x 4 L$ n% Y0 I# h1 J4 H T
÷ divided by
4 E3 k! d r2 V; J, l* Z
6 Y, s; q* B9 E% o 4 [- L. Q4 K; {, s; t
= equals; is equal to
/ p* \- v: {0 ~9 S2 {
! H4 d" e r& ^
8 ?. H& n- V' @; q! j/ [ ≡ identically equal to
; r$ V) a) u1 {/ r5 M* l( ~2 M
# h( _& P, p5 k4 U* f5 S # z5 E' e2 r& _; b" E, j
≈,≌ approximately equal to 6 b9 A j* K! h7 j9 E
" E; K$ s* t5 U; ~) H# W4 p
' X- _9 R# Y+ Y8 t > greater than + w/ H( E; E( X5 q
1 }1 |8 w, F) \4 Y* T
+ `! B L$ P, P) B ≥ greater than or equal to & `- }* i' y) u3 x# V2 L
* P7 u# m8 a( L0 `* v' E2 h
[& W: G' B q4 J+ P < less than |7 @* r5 l# v/ N
5 O; g3 o9 C+ H* s" s$ |$ Z
$ ]. z' G5 z0 Z) E( j ≤ less than or equal to 4 P; \0 L4 f1 i4 n
3 t/ ~6 o6 O* V& l9 h
" b0 S7 \7 v' m
》 much greater than
7 g, G O( Y2 S: I6 w2 e4 N" }& V
. h, J3 v7 ^! ^9 b
, t; m5 F( I4 f5 S 《 much less than
; k* ^2 F7 S. O1 @9 p3 |! _
5 t* b( d: C) g9 [) v, m, I
; D( R2 n' f9 P" r square root 5 p; H4 t- ]7 \/ h
5 x$ k* V$ t' o* }
6 q2 O I1 F4 k$ H9 ?) v& y cube root
/ t( z0 p$ K, o K* \3 h9 o( g3 }+ p. @6 o9 Z: F+ n
/ C9 i2 x8 w) ?5 X/ n1 e0 }4 Q nth root
8 W( H7 Q3 c0 O0 `% J" ~" T3 K5 K) f! ~% A
, Q6 C' ^$ F/ z6 G% z1 v6 @
│a│ absolute value of a
# y( s6 D% G; _5 w# I; \* p/ D L0 V# j$ W
3 o% `5 `. v/ d) K; N: k | t) |
n! n factorial
$ Y3 t4 n! N: s: r! ]# K
; {3 ~ ?$ R$ O1 w! G8 m! I 9 w: }: f7 }; F+ b
a to the power n ; the nth power of a 7 C6 t- R6 E* B* C* o( E: K& z
' x& P8 e- _2 J8 y- y. x" c
9 \3 d3 C8 r U0 y
[a] the greatest integer≤a
0 |0 b2 u" D2 V- D
* o6 H( s0 L; K* A* E( v9 U
3 K4 W) P2 ` I) q9 v& y! Y4 E the reciprocal of a
* |& i1 n4 q2 k0 z' [- v1 _# Z, {. Y
9 A" G8 f3 ~ [5 |1 ^0 b
P. _" |) l# O0 ?) D9 y7 n( I- h' h/ d( s
' q& g2 M6 v. u
Let A, B be sets ! d L! Q$ C! z, \
/ Y5 i3 `" l# M. V$ y
- i) e5 R8 U# f& O3 D4 N/ w
∈ belongs to ; be a member of
; i( T; l% V+ [0 }4 e! e
, ]+ d) @, x! e9 ]+ ^! j6 S ?
; Q2 \3 ] |, |! M1 U2 k not belongs to 5 |* j7 w, v% }- {/ ~$ d' s
* H& x# a, }2 y* P& [8 w
# d9 Y- i0 g* n4 i( h x∈A x os amember of A
# G2 x0 z4 |/ \& R R
$ M. a0 q/ |% J2 w+ |, \/ f, \ ; x! i" v" G5 D' ^* F; ?) J9 n
∪ union 2 B( `1 m ]% V* h3 m, u! I
/ {7 n& `. n! ~0 ~. O0 a
% {8 L7 I S6 q& O+ y A∪B A union B 0 ^0 b# q( {6 m T
, P- }9 g) r4 T+ b3 r* ]
' O6 o/ K5 E. @! k7 m3 H* y ∩ intersection 9 b! F* r& d8 p& b6 U3 y
9 k/ Z. ~1 C% s; Y. j9 l0 ^
3 a8 A, x6 ^4 i c2 g8 t3 V A∩B A intersection B 9 Z6 R" y( ]# ]9 J$ g! T: ^2 m
5 _, E1 f; Y, v
9 ~$ P6 @# Z6 S& c
A B A is a subset of B;A is contained in B
$ X- ~+ F/ |6 b& p$ z" t
$ m; o, i7 F8 b6 ^1 j
6 v( w, ~- P6 r1 x A B A contains B
+ |/ v+ h3 u; H
2 ^- T Z+ {- P
' y" L5 o# K% ]# G. C' C' l complement of A
: ]* r5 K' N2 q: j9 S9 i
0 ]" |7 t" x: b* C4 G- z$ x
: g$ X( k' ^0 T9 v. V7 Q* P _- G# F the closure of A " p4 c+ Y+ y+ w* O% r
6 G' R- c0 T& e3 E3 ~& ?
* J8 F. ~7 V' n/ R8 e0 ~9 p# d" ?
empty set 7 Q0 w9 T3 q! a/ e
/ H9 }) D1 \; Y
& k- t V% \ |; y
( ) i=1,2,…,r j=1,2,…,s r-by-s(r×s)matrix
" ]1 Y- w' A! _2 z+ X1 l5 _' ^& G! \: P
% B+ G2 `. N+ n8 r a
│ │I,j=1,2,…,n determinant of order n
8 f: K* W5 [# q3 ], y, D7 |7 N) r' M* n! @
: H+ i9 g: E Y+ h, w det( ) the determinant of the matrix ( )
4 \5 Q* @( z6 }; l& r. S# J! L
}: _" U! V( A+ H' g9 I
- l$ R1 t; m( ?) ~ vector F . ?' m/ } \6 d8 y/ R% }0 ? S
' b6 j# U, r, f3 \4 m$ e: c3 c% W
8 `$ t+ i. p e2 @ x=( , ,…, ) x is an n-tuple of
q5 B& |3 |: r! i A, u
0 j, t$ P2 y) u" K T# Z . Q1 u6 a# O Y- a2 ^1 q+ s* {
‖‖ the norm of … 8 t* d2 P$ T4 w; ^* m* o5 e7 x& b( y
1 Z. P: L! E" p
( a3 q* p% i+ @
‖ parallel to
! C4 a5 D# X# `3 a7 r( c
* R+ K( ]8 ~/ x9 d. W2 Y) U( ` # s3 l: r, h/ \7 q- f: [
┴ perpendicular to . W( w% T3 d9 [3 r7 r* E/ x( X6 x! V
/ r" b/ r" m% Z$ T2 Y2 N
# {1 ]$ {6 Y2 ? the exponential function of x 9 p) d. Q5 s, S$ j1 P% D9 X* ~
* x* R6 @, T$ x4 m
+ ^1 Q% g5 W1 `. P lin x the logarithmic function of x 5 U1 k" [) S5 { Z
# V0 C% k, V- N
" f. P5 t! g1 h$ D
sie sine 5 P: r l; o( O) F L& J7 r
: w2 O3 a7 U" @' ^0 i- r+ e4 g' W
" ~ q- T. h+ t cos cosine * I; m- J: @% D
2 E& I- E3 ?8 d+ d
x& Y j: H4 \6 \* \ tan tangent , `: i/ D+ P. ~$ j2 }1 G4 [
' n {+ e" M. e4 I* V3 r% l 7 T) l8 A. O, z& I
sinh hyperbolic sine
% {/ X8 d# F. y9 }/ R) ^6 A5 Z. r7 e/ M5 u0 @+ y/ u3 M) ?& b8 n
6 w1 D3 b: { L8 [
cosh hyperbolic cosine 4 Z6 z, A$ T. K% y) V2 g
: |4 z$ @& e8 }
9 Z9 @5 c+ @* w+ M
the inverse of f - t) w+ H; P- ^, K$ S9 j# \
8 A' ^3 u l4 Z1 ~# S. M 0 {2 u# K, a2 h
f is the composite or the composition of u and v 5 k! ?6 S5 o0 @: n+ w2 ]0 n7 O
. {) `1 C4 _; |! g# C6 b, I/ M
0 ]2 e* Q( R% E1 a9 c the limit of …as n approaches ∞(as x approaches ) 1 B$ \. _& F) L* M
$ A% }% S. p" v/ g1 D
- B9 R9 G A- |4 C1 w, J" c N x a x approaches a
9 z! X: I/ N$ D8 I( M+ v
7 @6 y( ?+ _6 L* j% R ! \4 ~0 E/ J* r* T- e+ O' n ]
, the differential coefficient of y; the 1st derivative of y
5 g, Y3 t9 N0 @0 M9 q6 A
% B9 _ C4 L0 ]" S* s$ N 5 g; O& s& u- ^- Y: T; r
, the nth derivative of y
6 R# }2 |: D+ n- a# K! V4 y" M
. f+ ?% t0 h9 {! n * Y% Q3 g, Z% M3 s/ |
the partial derivative of f with respect to x / P' i0 n S, D4 _$ ]
1 R, ?% ?6 v+ t, K
3 G9 g- Q2 @1 H, ?8 `. Z- ^
the partial derivative of f with respect to y % I: V; V7 y. S+ r, T; e$ {
1 y3 F* z3 o2 |# ^0 | 2 T" {; R w! V
the indefinite integral of f
+ m" t5 a1 n6 C6 q: c2 u# P9 I- i. F
6 l' K) Q% z6 R
the definite integral of f between a and b (from a to b) ( J9 d, R5 J- O" E: G
: c$ M* Z( F% b" P2 R3 a 9 ] V) Q5 L) C' P! b
the increment of x + B: m$ p ]: D6 c) G3 Z `
- |. @* \& G' @* L( w3 w; T. m
$ b, h! y% P+ x4 R
differential x
% k% E+ ?1 S1 L' I
! ?* b- j5 _+ n7 q # g0 r0 `! Y' Y) t
summation of …the sum of the terms indicated : T5 s8 j7 d8 a4 w& O+ }
9 D3 n/ R0 @, Z V o+ c6 X% r# b, ?
' v. S X- l5 k. y4 L ∏ the product of the terms indicated : D# L# S! G5 D; x) ^- u+ N
" ~( T* B# \8 y% R# k4 s I8 r
/ v2 R: m9 A: L4 R8 ]7 p; A
=> implies $ d9 Q0 d& K3 {' H+ S* o: `
+ ~, k. B. y; O% q; S5 k, R , Q- Y0 D1 `) O; j: ~2 m% H
is equivalent to ) E7 U! t8 U2 ^+ @! A
4 Z& s" ?0 b) @. D: X 7 C7 F/ `4 |- B( |% ~
( ) round brackets; parantheses # h. S0 Q3 O) x( g0 K+ u! l+ @, n% Y
8 {5 J4 s) n: t- A: c
' R3 P& _' T8 R$ A5 R+ |
[ ] square brackets ' o, z" o% @; G6 F" p# r; T
& P- r) N. F. {( y8 a# y8 ]6 @% P
3 e* g( K2 Q" E4 g1 @ { } braces
* a; d; G& i' R% |" O; j9 S W- v, V& f6 |5 r
# n2 ] M- }3 X7 p, X) F! l 4 w9 ]5 F0 H7 V, q3 v1 \7 V+ G0 b
4 E- S+ E5 h9 }9 T) w& D0 ~
' _ j! b& D) Z) ~$ @ A' c% |! x ! R& @2 I) B, J2 l, a/ O& O. [
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