如何定义数学用语

kidd0323

如何定义数学术语?

（How to define a mathematical term?）

0 F9 a7 G# Z. k& Y& j/ v

1.
  U2 U8 @; c( x& \Something is defined as something.

( e" A7 U4 x4 BSomething 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.

The mapping ,is called a Mobius transformation.

2.
/ H0 @( F1 D, {) [: J- N$ r+ g7 VSomething is defined to be something (or adjective)

' ]0 p) \# V1 ]! G9 nSomething is said to be something (or adjective)

) ?7 k8 j& A( @" e2 r例如：

The 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.

3 i" }* S8 o1 Q, |Real numbers which are greater than zero are said to be positive.

3.
We define something to be something.

: ]: K2 n/ F) @% WWe 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.

4.
! a; D/ d) H: l: P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：

: ~  K2 c7 \% u9 q& E. OLet…, 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 .

: x" J8 f# w6 k! o' o: fLet d(x,y) denote the distance between two points x and y of a set A. Then the number

0 C4 u3 q) }( \/ s: _, W  W6 t& X# b

is called the diameter of A.

. ~* c' ]* V7 A" V; a

5. 如果被定义术语，需要满足某些条件，则可用如下形式：

If …, then …is called …

6 e4 C' K/ J4 HIf …, then …is said to be …

+ [6 l' d# y+ X) |( ?6 gIf …, then …is defined as …

If …, then … is defined to be …

例如：

If the number of rows of a matrix A equals the number of its columns, then A
, X; s) m1 P4 u+ Lis 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.

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：

! Z9 i3 I0 ]( f% A  x' F8 RLet 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
z1≠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.

' e; j3 p, V1 _3 V: [  x- `

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：

Let …and suppose(or assume) …. If … then…is called…

例如：

2 f5 i2 s( u( A* ]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
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^^