数学专业英语-Notations and Abbreviations (I) Learn to understand
- r/ j1 N& P+ Y- I 7 g3 ]* ~! x, G
8 E" L, i4 c1 g# I, g: H* Z
- L- D1 P3 n9 R9 G1 W1 Y& j8 m: ^
; X/ o9 G! ?8 l! F7 ]N set of natural numbers
- s# B o# o4 J6 [3 g/ L
4 i8 T7 f" n; a, B4 v3 t3 D+ t! [/ f1 u
( g1 u; Y7 S3 o$ C! H0 y4 D
% }! ^$ h7 j% J7 o Z set of integers 3 I# D7 E9 H1 z8 r2 D% d% u+ t
4 u4 a7 o: R T; R9 v
& C% N/ ]' r6 G" e* C& e2 X) d
R set of real numbers
) Z" m p' q& q4 P8 U- E
4 h+ `' v" m3 G1 Q' T- g& }2 a# e
5 M4 M4 a4 ?# H6 t K. T3 W w# y( ^* u C set of complex numbers
8 D8 y" }( K% E+ u- l8 V- c
1 a, Y' N% G! m7 |: w 9 {7 N& U |6 u8 p; `: e4 k
+ plus; positive * P1 e- B" O4 c
( T/ b$ {" d3 F# V" d( R$ u: Y
% R& w) I8 c; Q7 Y% h - minus; negative : ]$ M0 H3 I& F) ]; ?6 C2 f
5 S0 w0 Y# J/ `& Y
8 \* u. `. B* L( d6 {, V" x+ t. o
× multiplied by; times
8 C! {0 e$ k4 ]6 n$ G; h2 u) h$ X# |4 {
4 _6 a( u8 V4 Q7 f( o3 ^ ÷ divided by ) I6 F) @; U# G: E) ]. C+ F; {5 w
; ?; [# e/ T7 M# u
' e* e4 P- C: G7 r, X& A& U = equals; is equal to
?# W4 u, [$ ?1 t# U$ L# j; D7 \7 Z3 L( T1 u$ D
; T' r7 \7 F1 R0 w
≡ identically equal to , e( y5 X4 B+ \5 Z
$ F: C; k0 D. k: Y9 g- i
4 v; H+ s' ?% w& V* P, R' y
≈,≌ approximately equal to
' C- O2 w9 o3 r A
' \4 x: O" _4 B) A
' R4 Q& r n A- B! Y0 \4 H > greater than % ~0 A9 |6 ~# V/ G& G
6 n6 b& z6 ~# q1 u$ X
3 g% \( Q7 k- V* L2 E7 ^ ≥ greater than or equal to
2 O9 w1 J; g9 y9 E* J( [' q; j& `% q
" D- P, _# ?: N- ^, P7 o+ T
< less than
$ P# v. N6 L$ Z% o( u" O! f9 n6 V5 ^# ~; J: C
2 z$ y: O# V9 t* p3 ], N1 O ≤ less than or equal to
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# m" n4 f4 H9 w$ T) C- ~' c$ X
》 much greater than
3 e' O4 m6 T& S7 ^- ~' h6 ^0 C/ c9 ]- N
( F/ [( o% ~" r' {2 n- `. s5 Y 《 much less than 6 \: i' w# F7 [, T& J2 W
0 y, x* a( c: x6 M& y2 c$ i
2 k# r6 h: X4 H5 }" c square root ( {3 J* i" l1 ^
4 O* B7 v5 [. y; G+ k3 [ - L7 f8 `9 M: _: O2 U% u$ C: x
cube root
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, d# f2 {1 h4 ?
nth root 7 O. J. F( W0 K- g- ~, C/ b
' O8 s+ p8 ^# k. ^5 F4 ^
3 @( `3 f" q$ q0 C9 U8 g │a│ absolute value of a
1 N0 c3 G1 {6 j, ?
; M+ i* w, W! R& j# w1 m' Y0 L- r
0 g8 {( s% k: a3 x+ v. G8 y) M n! n factorial $ Z- c9 F$ c* Z: H/ E& u) F8 x6 Q- s
8 k! z2 e& C/ k! {9 h4 H5 Z& Z
+ T$ C0 L: U. b5 l" p a to the power n ; the nth power of a
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[a] the greatest integer≤a 9 ^) T, V9 `# a6 @+ c
; W" B7 ~ j2 h) ~8 G
1 E3 g, Z0 T' x* p0 F5 ^/ O7 `) \, g7 t
the reciprocal of a ) W5 J& j" ~- |% [, F
" V# `, `# a* D: T3 Z5 f
& z3 B7 s) e X# b( M % k* D- @+ `7 ^( a1 Y2 _1 N
0 b, v; ]4 F ^$ p' `8 g - Q8 N" ~+ M% W* J1 `1 H1 G7 F
Let A, B be sets
3 N; Z1 z( b, I5 `8 j) y+ G2 L( @9 X& ^: a/ L4 `0 \0 f& U7 {
- x O2 q0 b- G* u
∈ belongs to ; be a member of
6 h' K5 K/ }2 M1 \
, ?5 E! g, t& x; [3 p: O8 I" t 8 r+ {: S6 R* ~0 u: s0 j
not belongs to
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J+ g( i" x, i
; w* U& J4 C5 {" P( }; n* g: l x∈A x os amember of A # K# v. X- Q9 S4 S/ |
( y, a. Z! j" s& C% a 7 ^ ?/ m" k. H2 w
∪ union
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- ^1 w7 ~% Q5 j) X: o; y. d* X/ z$ q
5 k7 k z* u9 { A∪B A union B 2 q7 y! x# y1 O/ C' d3 ?( u7 o
" t% n8 }. n3 T1 M& u
* c7 Q: |& F: g# j6 V3 x, q
∩ intersection
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A∩B A intersection B " N) m8 Z3 @. m- N T7 ?
9 O2 g1 M0 _" b0 f
( y' @# J( V; C5 B* Z8 |0 g A B A is a subset of B;A is contained in B $ Q$ m( s) V \; y2 d: I- b9 w- Q
1 U) r1 A; v6 M2 D
' Y2 r5 B. t3 t# r1 N8 `' H
A B A contains B + M7 b- y* d' |: o- z+ v
* ]6 `( \, W8 M8 c$ `! W: j# U
0 U- ~8 y: ~: n complement of A
: u1 o L( d* @. c( p+ i0 z
/ M; U4 v9 Q1 c8 F- G+ X: H ) p+ F. I: S9 t6 Q( l, d3 [$ A
the closure of A
$ A! G; j5 ]; g: V: ]- k" r! m1 u: C. [8 l4 ` u2 D
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empty set 9 v8 q- T* H- j- e
+ w5 \/ C, m+ S( o. n 7 g8 d$ s3 n2 j4 @
( ) i=1,2,…,r j=1,2,…,s r-by-s(r×s)matrix
% a& ~+ U& e8 d
# y' b" b, O; v& ]! t
2 z, L8 u3 r2 m, M9 S6 H2 I5 L │ │I,j=1,2,…,n determinant of order n
$ M. @ D, \% R0 h' F( W4 q( a! L# m8 B: | i9 a
! v/ k) Z. O4 v6 m( s2 x8 l) l& s det( ) the determinant of the matrix ( )
4 U! z4 E K1 L. A2 j
6 U: R0 J7 Y/ d V* l; ]) r/ b - W- s' S' v3 J5 }+ N; i: ~
vector F
, V3 |/ `4 X" p1 I. R; ?# K# X# u6 d0 s% P' l
3 f; Y p; Q, C0 ^) q/ g* B6 V x=( , ,…, ) x is an n-tuple of ' H. k5 R0 O+ f+ l# a
- [1 [3 D. v. H* A/ F' v
6 W) q$ v9 x. K" w7 h
‖‖ the norm of … 9 o! P9 ^& u7 U$ Z* k. D
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2 P" I6 e3 @7 B) u' T/ ^' r% Z
‖ parallel to
; ]. m1 h% K' D& [$ ?7 ~; \% }, b( Q/ b" ]! m
: p$ B$ r" Z# B1 Y- _- ?, @& U$ c ┴ perpendicular to 2 X# D+ j) _9 {
& `1 ^4 t) L7 |6 S) M# d: a 1 G0 ]4 I5 v1 R6 C) _# W
the exponential function of x . B. a2 _& o7 B! G' l; n0 i
' b, e6 m4 e& G" W0 h' e0 L$ F7 s- A
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lin x the logarithmic function of x
: ?; h+ T% w# H/ ~) \2 h8 Z
' k |. q& j# l* M- Q+ O- g
7 @; L. k- v) n3 w$ r sie sine
; d U$ w" _$ J* t2 C* Z& R" A- H. Y( o6 j4 a
, {+ m8 B' i C8 i7 p cos cosine
0 v2 |% Q5 y k) v+ ^
0 [! T9 M4 K6 M9 L$ r % s, t1 G9 l; o8 O
tan tangent 8 y7 T7 I" s g1 K6 |, c( n
3 q- P4 M) U8 p H; `
* f1 Z3 S9 L9 h5 K. s: b sinh hyperbolic sine 8 e4 y/ |4 _6 p8 o3 e% t2 C3 N
. k) s4 v# A' p+ k8 }2 j
) U5 e& _6 G4 v) j2 L8 x9 s9 D3 B) ^
cosh hyperbolic cosine
8 N5 H2 R4 L9 d5 Z0 }1 L# x) X: g9 E" T& S4 ~
4 c6 N* j8 S; C the inverse of f
5 H: T5 J9 h) ~3 _2 f( b J1 E+ t1 {. ]7 u E5 A( T$ N
R2 n2 E5 K# v E3 `! O6 h f is the composite or the composition of u and v
+ c+ c7 S8 l/ Z" ~3 A' ]' _- N3 G
; K! U( g+ U7 F+ ~2 `1 m
4 y5 ]9 i+ o( R# f. W2 e! S+ ? the limit of …as n approaches ∞(as x approaches )
& a2 _+ F+ `8 \3 A! \
) ]6 k, _/ v' r: E7 k4 P
# I" ^/ B, v0 ?3 t3 x5 h; G1 ` x a x approaches a 3 O' i# c% U! {5 _7 J3 ]# u8 x6 a) C
7 e, B( w. N9 s; h4 l, Y# U; Q & ^! b A% ~5 L9 t/ B, A. ?) a- ]3 B5 C" n
, the differential coefficient of y; the 1st derivative of y 0 a8 {9 D" W( G
; d0 S4 p/ \6 M' d) g
( G& x3 _" s& f7 e( Y. O , the nth derivative of y
D# u2 t' Z! Y" C; N# s+ a& C0 q: x: U! k' q
5 v( m. I8 q% I1 }+ {/ A
the partial derivative of f with respect to x & Z7 B" Z8 M* Z: C
' e/ W7 V! a, t, ?( Z6 I
- O' Z: ?9 ~# W6 u the partial derivative of f with respect to y
! W, _( m( p* c5 e. G8 `5 T
8 r, M4 m' J" E2 l7 t/ X 1 U) J8 M8 A. I% d
the indefinite integral of f
1 ?* N7 ]. s7 r; R% D" B& _4 y/ r
, }. W: ]7 S0 B- L3 h- ` the definite integral of f between a and b (from a to b)
% \. r$ o' b0 m! Q: F; S- k! M; e5 `+ ~% w! C
4 i* i2 Y7 {5 ]7 K. T, t8 ` the increment of x
9 i7 {: o9 m; F o. W; Y W
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' ^ _% C5 p+ @( p( ~% s differential x
% ^0 X6 A# P5 O# h4 X/ A6 F! n8 Y& }- K# A- r8 m
- d! [) f6 ~& F. E
summation of …the sum of the terms indicated
, C/ v! N# h+ G$ q) v- l- n# Z' B" H$ _( C$ l& q9 a
$ U5 T$ x0 t& g
∏ the product of the terms indicated
& t% a1 {, @$ D* K9 U/ t" s
' B+ N5 l: I9 U5 H& o) F+ { 7 j6 C; `, R* [
=> implies ; v& W0 Y* C3 d% w1 V8 `3 c
' v! ?; _7 m9 C" e# w" k
$ m. a' B5 m( O% C* a. u/ f is equivalent to + K" u7 d$ Y# y7 ~& s8 Z
9 G8 N& S- e# o
/ o! H& w7 P' Z: g, L" [, Q ( ) round brackets; parantheses + r1 ]9 b3 c5 w6 F! M I& M
+ w; ?" f+ ~3 J; M
u+ k2 n0 p, { e' }4 B [ ] square brackets c. R7 O8 y# O. H' C
# F6 G; t$ {, D1 `+ {
3 L% a# m; y0 E% e8 { F+ y8 T; l, c
{ } braces
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