数学专业英语-Notations and Abbreviations (I) Learn to understand$ H; {! R- x* y
& v- _' y# [; R# Y, c
( u/ Y" ?" ]0 O$ I
7 b1 @; I9 r3 I2 o% K6 z
* a- C' N7 K, K& o' n9 MN set of natural numbers
) c. ~4 }1 T3 J3 l, w4 @2 O8 C2 q
* X9 r4 L8 j: y! A1 J$ ?
; v3 B# q/ S. Y& K' G
3 F; T, R/ G1 d5 E9 A Z set of integers
5 V- x! c* H5 f8 N4 N+ P1 {- z
, L# k/ Y- ?& _+ |+ r: e1 b+ ?
2 A& L* P' a2 ?# o& M R set of real numbers
/ Z/ F9 `5 q+ \% `7 c) s9 t$ E& D; ^5 }3 v G9 i6 s) H1 |
* }4 {, ]$ `( T: f& Y# n" L; b! q
C set of complex numbers
- D' C* m0 C! {1 Q: k- A7 }+ ^" B2 ?
- w/ z% B6 M5 o6 F& X- \
+ plus; positive
( H4 E/ `) [5 E6 n3 y# V
9 [+ t& `; k) s6 c9 K/ N9 p 9 ]2 X6 f- a+ p
- minus; negative $ w3 |4 v- R# C' U' q7 p
) X3 U! v) l- b3 A
. H9 n5 V1 H2 X" w; Q" d × multiplied by; times % X: E5 u. l" x- M
5 [3 c5 X" _( ~' A* R# T- f
, ]/ V' S2 @1 G* D# i" a6 J
÷ divided by ! ^ ^) b! L, _+ Z, q+ l; s
4 H* C% y4 z+ ?0 `" s; l7 s E% u. \. Y: s6 O8 p9 ~
= equals; is equal to # o+ ]! A2 X$ `: s9 \2 O- E) t
9 d7 f9 ~7 ~9 `5 j/ ~9 `
& J4 m) y+ v: a; {# R5 N ≡ identically equal to $ i' q% i+ t/ X" S* y1 ~7 }. b" X
0 } w- _) \% S9 H' {; ^/ ~+ G
* E5 E8 y0 P' T2 p) l- M
≈,≌ approximately equal to
% f/ ^3 I) Z; q& Y" R# I! `6 l. i6 D& @
3 C8 ?5 a' }% v5 t > greater than
E9 K5 I' g% r( c, p2 k4 a+ ]' o7 W
/ A4 ]( n0 a: i2 h' N ≥ greater than or equal to
- Z0 i' i! S/ m5 O# J' Q1 s* r
6 G u4 Q4 C. D4 x8 \
< less than
$ y6 }% _. J9 b5 e
% o0 K& u% N0 O# a ' q9 S1 {$ {4 v2 L
≤ less than or equal to , T7 L! f, [- T% q( W
: {" O* D* Y* K 9 c; d; Z. Y: R) I0 a. \6 M
》 much greater than 2 m! {. R+ K2 ^/ f* `
$ s4 u3 C( @% c* l 7 Z5 n9 k' |% H5 T3 }
《 much less than * [' t" b; e, j+ n( a2 k
. ]2 f% w9 G2 }% q1 u
* C) x6 n) w# _' i- I$ [3 y
square root
! q2 h' d" M% `6 I- [" X
5 S% l* {) E6 n R x
4 q7 P% w4 \: D9 G' _ cube root
; R, u' S4 K+ e% r8 D" ?
: O/ q, L7 R" Y. Q2 ^ 9 T) R& X. P3 Y% H
nth root 1 v, {# c- j/ g. ~ O
4 F' K* O( ^+ c. o
' g* f+ j7 F' a$ D2 e: @2 e! V# q │a│ absolute value of a
5 b4 B. ] Z9 ]( ? o8 C- a+ w3 y) D; R: b( g$ g( q" m; g$ z9 i
$ D( b3 A. H, y: Q( H+ _
n! n factorial
$ z9 M4 u5 D; f# w2 B+ c2 n$ q" n: C1 K1 Q
$ B7 C2 c1 v; [ u
a to the power n ; the nth power of a
( y" {' i2 `6 d" }0 [4 M
2 d5 |9 X2 B8 X+ ~ 3 G2 T! g% }+ |( Y, }6 x0 ^; L
[a] the greatest integer≤a 1 `7 D; C2 {5 [& `8 i, |, X- R
: J9 Z9 x0 A% V- q P" Q: q! ~$ g; B& R
the reciprocal of a
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/ \3 I" I& g4 L1 \6 x
2 r+ _6 W$ d% B" g5 S3 D1 g6 g
2 k: i I" ?) \; y " Z4 a* P3 v8 Q7 W! n8 k
Let A, B be sets $ I5 ~/ e# {; B2 L6 [
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∈ belongs to ; be a member of
- W, W0 R" K! ^4 T$ i* S' \! D9 X/ m5 N/ r" g \5 @. p6 m
. c& k5 s1 p+ M6 j) H not belongs to ! c" V2 m) j% p9 S+ u" J
* ]) V- o F- j' ^# u# Q" i3 u
; A5 Z/ B% G6 i8 ? x∈A x os amember of A
7 {) C" l0 W9 l/ `5 q. m" `; [0 I+ @0 M. R; f( h& F S) c1 s; L! m
5 g* X# g( @! ` M8 ^5 D ∪ union 5 P; J, `6 O' R7 j
! f2 `) k; L* F3 u( |, J
$ o) B, X- V4 O: s* ?
A∪B A union B 7 F7 }' d, j4 l% U" s2 r
0 [- B$ ]- e' ^/ [
( y: m/ W7 G& b/ c5 p3 z6 s ∩ intersection 4 E. j3 p6 s0 Q$ w
) U% G) m3 p- V" N# {' S3 t * @, P' ~1 L) [
A∩B A intersection B
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" U& }1 R' S% a A B A is a subset of B;A is contained in B
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6 w# b4 A+ S4 q. T7 q! p p- @; q A B A contains B 3 {" x$ j ~) K$ g7 M* J9 T0 Y
2 g# S7 O5 J! ]9 x& v/ Q
3 H# ?8 f& h7 n- I) i; u complement of A
9 u" t9 G9 ~7 ~( g) n
0 G) w6 e* U1 m7 l! a/ p 1 Q6 s: U# v8 ?
the closure of A & f9 m/ j! G0 N+ l2 q h% Q& T# Y6 L
+ q% o9 l( U- }& O; `6 d4 @ ! A/ X1 T g( Q( [% i3 v
empty set : }% f8 a! Y+ T; s6 n8 R& B
; ?% B! U) n' n4 \* ?" r# W! ]3 ]0 _3 V9 d
" X3 }9 x, {/ f7 N ( ) i=1,2,…,r j=1,2,…,s r-by-s(r×s)matrix # U; f$ z, z) B4 n- x- x
! V8 P6 o) ?; O8 y$ {/ T4 V, u t
8 Y3 [2 |& ]& }' p5 V │ │I,j=1,2,…,n determinant of order n
7 t" C; S3 g* Q# U8 w
$ t7 n ? a# w# ]% l0 u4 y
9 Y* X& _) k" p$ i det( ) the determinant of the matrix ( )
8 P* s' p; @6 H) [, ~- Z4 C) L
* G c5 d" b8 Y% V! V 7 Z. E z+ K$ K) i( J% S' i
vector F
2 i4 G( f) f3 O! {/ R% M. [7 r' ]: \1 @6 p2 E( n- y) W9 j: P
8 A4 r" Y# [/ J- ~" j
x=( , ,…, ) x is an n-tuple of
% P3 s E8 N9 a% u) }+ K5 u$ T( X: D7 M( T/ [2 `4 T
3 a! k, {+ [3 N
‖‖ the norm of … - }) U* M& f1 n1 e" n' { Z
" F0 \/ N0 [1 S6 ?0 ~& ^* `
9 N( ]; g8 f! e( L ‖ parallel to
4 Z) {: w; u4 p. O2 K( h% P; `: ~- u5 x( N" y) J0 A
2 O: Y4 Q+ {% d% A$ S% E ┴ perpendicular to 1 }, K5 l O: _6 \0 P
' | S2 J$ D+ s1 C" J* c
' U/ b6 t6 ?, i2 R
the exponential function of x - u" c p# l2 j: @( s i
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lin x the logarithmic function of x
1 o" T1 n& y' a; q
9 T. e1 |1 A/ m" J- l- z3 y
2 p0 I3 `1 c }* a$ x sie sine + |3 ]% _6 A! q7 L2 R2 n5 k
& J6 c, j3 C. F/ [7 ~ ! P0 ]: X" q, C" c
cos cosine
0 }, R+ o: }2 a. b& [3 N$ r( Z' Q5 o6 o3 A
( y" n3 v- ]* L, S
tan tangent : h, m7 z4 E8 v0 ?$ [7 n/ j: f
- o. U" q+ J. e
' z! i9 G" {1 }* @7 e0 z9 e! K; } sinh hyperbolic sine ( s7 q' j4 V9 n4 c+ G
& g( F# A& q. O0 G3 z9 c0 d) b - W2 _/ z5 }/ {8 l* d6 I! |% l$ K
cosh hyperbolic cosine ; {+ n5 _( }1 c) w
1 J" e" r1 i" | ^2 l% s
Q& V5 y* T! @1 O$ l- ?2 w
the inverse of f
, q0 v& p5 O) E, H! q9 |- s0 U v2 ?% H, e
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f is the composite or the composition of u and v 4 h; b: r, w" {: g* Z
& d: _* y% ]* J) ?, y
/ D- j* l3 r3 ]
the limit of …as n approaches ∞(as x approaches )
0 y4 i7 E: o) A7 s3 l! R3 U5 T6 F2 t& S* _3 q# O5 i
0 n. U! f; ~! U8 f7 y x a x approaches a C% k- M2 K" {) U
* @8 q' V0 N$ H8 d1 U/ r
, j0 ]! \: O- e; R1 l5 M( { , the differential coefficient of y; the 1st derivative of y 9 m5 w' ? g& L
w8 C8 F! f$ R6 {2 K
; Y k+ {; b) S; }4 q G( X3 ] , the nth derivative of y
: [8 _) X5 u& z( k( m$ S
$ y( U+ r! L4 a; m8 ?
9 T: W1 I( Z9 O# z1 X; G: `" b6 } the partial derivative of f with respect to x - m7 B: g6 O8 C' X( A, v
2 m y5 Y6 H2 v$ Q
3 N) l9 L8 z2 o/ Y, W( Y' ?4 S. u the partial derivative of f with respect to y ; t+ b& |4 ^6 c
+ ?/ Q N& ?6 Z6 N 8 u5 g5 q( Y2 _ R* L" P- o' d: j
the indefinite integral of f & z+ ^# p1 R1 ?- Y
' X5 @: a$ i) \) L9 r: I * W; Q# \: {! \& c+ e( ?! A
the definite integral of f between a and b (from a to b)
, {; `) A5 n6 R# l: p) w
. N3 c$ \; |3 A" B' L# X9 H b" R , o6 [0 }0 S9 N8 d6 }2 t7 _- _
the increment of x
D/ D8 ]9 [, Q$ q# [% f1 [7 \9 F* O4 r$ D4 N; v
8 e7 s! n1 i% J6 K) m
differential x 7 Z# V% g% S; h) y2 _) [
$ @; K% A7 T( o* v3 _& T
0 Z" @# H" p; a$ s5 G summation of …the sum of the terms indicated ( X4 e2 `' ~6 W& _- C
$ H8 i; q5 U3 Y# F0 K
5 h, ^4 b' ?, O/ {+ s- `/ G: H9 J ∏ the product of the terms indicated ; z1 @ y. A( q1 A6 d* b
5 z$ V5 D& x0 j0 M8 B * }' J* c0 P+ |# q! d5 x# }
=> implies
0 U4 N) O' H* v! X) n) X2 R" A; J3 H- _2 V. |
6 b/ J8 f: ^2 ^. d is equivalent to & {7 {% v2 C0 \* @& C; N% Q
8 W0 ]' y( r; w) L p4 W/ a
- M! {" r1 P; l
( ) round brackets; parantheses 1 O4 a# B1 ]3 M; n3 a% F
* t" h' a' f3 o 4 s' [4 @6 w- d
[ ] square brackets ; M7 H7 l H1 W& O
h) P( ^9 w Q1 `& g) f+ i8 G
! t# C# |: T( @( W { } braces 9 R' [$ G3 w: G
4 j$ Z p8 z% {" c4 H ) D) l$ D) J! T& i5 j) x
1 C6 E$ ]1 ?0 m) {: _' y+ L& ~+ b3 B7 B* X
- j. _' Z: s; y0 C3 S" Z5 Q) a1 K m1 Z
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