如何定义数学用语

kidd0323

如何定义数学术语?

（How to define a mathematical term?）
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1.
Something is defined as something.

9 ?0 d" e* S6 F  d9 f3 DSomething is called something.

5 P/ D2 R' C% |' i0 N% C9 {3 Q' m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.

( Y9 w/ h9 L0 q1 }6 ^9 u+ lThe mapping ,is called a Mobius transformation.

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

3 ~2 g& z  @8 t+ H! V$ c7 v3 CSomething is said to be something (or adjective)

例如：

3 j3 S, E* }: I! u' q" ?The difference A-B is defined to be the set of all elements of A which are not in B.

5 _3 Q7 ^0 z- [- cA real number that cannot be expressed as the ratio of two integers is said to be an irrational number.

' W1 p/ n3 ]% |, a, XReal numbers which are greater than zero are said to be positive.

3.
We define something to be something.

! r  j2 H9 ^( tWe call something to be something.

$ m' F$ f9 o$ G& Y7 b& S8 v5 v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.
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：

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 .
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1 e0 h: n& O- aLet d(x,y) denote the distance between two points x and y of a set A. Then the number

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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：

! F% k# h9 Z0 W( t  ~If …, then …is called …

If …, then …is said to be …

If …, then …is defined as …

If …, then … is defined to be …

例如：

; O$ ?5 s( x/ |) y- uIf the number of rows of a matrix A equals the number of its columns, then A
is 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.

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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：

% P2 F: l( t0 E* W3 w& [# i6 z6 ~0 ELet 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.

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：

' W2 d. G* z( v5 y2 wLet …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
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^^