(How to define a mathematical term?)
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( A4 N2 X1 F% @& O- OSomething is defined as something.
N3 p* H$ ^. ySomething is called something.
The union of A and B is defined as the set of those elements which are in A, in B or in both. % m7 g0 w* J9 _3 [
The mapping ,is called a Mobius transformation. 2.
% K8 t0 [' Z* VSomething is defined to be something (or adjective) * ?6 M- ~" y; m& _
Something is said to be something (or adjective) ( G! A, d1 M2 q; H, a
The difference A-B is defined to be the set of all elements of A which are not in B.
: _8 F' [' t% v( U) j9 eA real number that cannot be expressed as the ratio of two integers is said to be an irrational number.
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Real numbers which are greater than zero are said to be positive. 3.% p% S9 D& y- s4 ^" N
We define something to be something. 7 q- [: s: K [) h! P
We call something to be something. ' p: ^9 _7 T+ Z* `! q& N
例如: We define the intersection of A and B to be the set of those elements common to both A and B. / l7 X' F) u( s! T& P5 j3 x& ]/ C
We call real numbers that are less than zero to be negative numbers. 4.
. j$ b& Q6 M* \8 R/ \* k: T9 @( y如果在定义某一术语之前,需要事先交代某些东西(前提),可用如下形式: # w1 _% N) A$ p! s. f' U
Let…, Then … is called …
( [) ]. c' N6 i# }4 _8 X" B( FLet…, Then … is said to be …
Let…, Then … is defined as … Let…, Then … is defined to be … Let x=(x1, x2, … xn) be an n-tuple of real numbers. Then the set of all such n-tuples is defined as the Euclidean n-space Rn .* n( h+ T' x, i& Y2 z
7 z5 P/ H3 O: s" w7 ~8 w: kLet d(x,y) denote the distance between two points x and y of a set A. Then the number
is called the diameter of A. 5. 如果被定义术语,需要满足某些条件,则可用如下形式:
\( x/ y6 \- g$ a xIf …, then …is called …
* t3 O4 W' D3 k( Q* ?2 W9 `. I+ X, p
If …, then …is said to be …
, V0 _+ ]! V4 |4 ~3 I7 x: Y
If …, then …is defined as …
. u6 Z' _+ r: J9 x6 M2 xIf …, then … is defined to be …
, T0 {+ y# B# Q$ B; B/ dIf the number of rows of a matrix A equals the number of its columns, then A
- u* F' X! s$ I9 }# C2 X6 ]is called a square matrix.
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If a function f is differentiable at every point of a domain D, then it is said to be analytic in D. 6. 如果需要说明被定义术语应在什么前提下,满足什么条件,则可用下面形式: 8 N& k; Q% C9 E7 h i7 {7 Q
Let(or Suppose) …. If …, then … is called … Let(or Suppose) …. If …, then … is said to be … ! Z4 Y* z7 y$ l- t- {. m+ G, Q
Let f(z) be an analytic function defined on a domain D(前提条件).If for every pair of points z1 and z2 in D with
' k* C" R$ g6 x% cz1≠z2 ,we have f(z1)≠f(z2) (直接条件),then f(z) is called a schlicht function or is said to be schlicht in D.
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7. 如果被定义术语需要满足几个条件(大前提,小前提,直接条件),则可用如下形式:
( H) F7 Y6 O$ u$ ]Let …and suppose(or assume) …. If … then…is called…
8 \4 a; N" l+ w) h6 x! sLet D be a domain and suppose that f(z) is analytic in D. If for every pair of points z1 and z2 in D with
; P5 W1 j6 q3 m rz1≠z2 ,we have f(z1)≠f(z2),then f(z) is called a schlicht function .
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