如何定义数学用语

kidd0323

如何定义数学术语?

（How to define a mathematical term?）
/ o/ [) d8 r$ C; g

" ]8 _7 o9 P5 p( q: {( g, j9 b

2 F- T' P4 u: ]0 e" d8 ^! ~

1.
Something is defined as something.

% x- U- |: @3 a/ U. nSomething is called something.

例如：

    The union of A and B is defined as the set of those elements which are in A, in B or in both.

! g& h  m- h$ u1 v: bThe mapping ,is called a Mobius transformation.

( ~* K) f& J8 p1 k5 L3 A* ]; w9 S

2.
Something is defined to be something (or adjective)

) y4 l6 q/ ~" g/ A5 bSomething is said to be something (or adjective)

例如：

! z( I7 P9 M% h+ s# O. g9 EThe difference A-B is defined to be the set of all elements of A which are not in B.

A real number that cannot be expressed as the ratio of two integers is said to be an irrational number.

+ V! D  I& w: |) ~- dReal numbers which are greater than zero are said to be positive.

3.
) p4 z1 {+ s' Y. O8 h* V: v) \We define something to be something.

; e+ y3 ^- ?# C0 M( {# JWe call something to be something.

例如：

We define the intersection of A and B to be the set of those elements common to both A and B.

We call real numbers that are less than zero to be negative numbers.

" V  `: Z) {9 `8 }7 x" r5 T  I! R$ m

4.
& e1 l/ d# @8 H$ a9 Q- O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：

/ B( k7 N/ \2 p4 [Let…, Then … is called …

Let…, Then … is said to be …

Let…, Then … is defined as …

Let…, Then … is defined to be …

例如：

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 .
! H0 c. ]! T1 a+ c: b/ T

Let d(x,y) denote the distance between two points x and y of a set A. Then the number

& {& h, g, w- J

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：

$ ?# j0 ~4 b/ C. K( {If …, then …is called …

$ W3 _+ V- B' D7 s
; B7 t* w, `: L4 oIf …, then …is said to be …

If …, then …is defined as …

' {% F. H, k% I( K8 G! L) y1 nIf …, then … is defined to be …

例如：

; R$ S( @# [9 a* XIf the number of rows of a matrix A equals the number of its columns, then A
  Y) n+ ?4 a& cis called a square matrix.

If a function f is differentiable at every point of a domain D, then it is said to be analytic in D.

. i" |4 W  B7 c5 {

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：

Let(or Suppose) …. If …, then … is called …

Let(or Suppose) …. If …, then … is said to be …

例如：

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
# H1 ]8 s' e3 uz1≠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.

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：

) }, s) P0 I, K$ gLet …and suppose(or assume) …. If … then…is called…

例如：

Let 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
4 ^% h: U; o* B$ h! T  s' |z1≠z2 ，we have f(z1)≠f(z2)，then f(z) is called a schlicht function .

许凡

还有没有更多的啊

zhenghui999

henhao    henqiang da

zwt1987

好东西哦，分享了啊

joyce19880122

太好了，不用花钱。谢谢谢谢～

凸眼金鱼

分享了~~~~

KaloDark

楼主找的就是你^^