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.
: I0 \8 d! S1 s: T( OSomething is defined as something.

, o  e$ x: a. p) M  Y0 V' |0 Z9 l; FSomething 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.

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2.
' b) `0 j* H! |8 O$ aSomething is defined to be something (or adjective)

Something is said to be something (or adjective)

例如：

& l1 X% z# g3 R" _6 x& YThe 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 n6 l  ]: P3 M# J% ], f  E, uReal numbers which are greater than zero are said to be positive.

3.
We define something to be something.

We call something to be something.

& a5 k* F% m, x) _# O6 Q# e7 u例如：

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

! d! c7 _3 N( D9 j5 cWe 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：

- [4 u& P4 c. a  NLet…, Then … is called …

* s7 U! n+ M; o2 FLet…, 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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3 S! f7 O8 y9 J' y  h4 }. w. gLet 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：

+ h, |+ L% q% \0 y6 N# U6 |If …, then …is called …

. z# V3 n" P" h* A5 ~7 g% S7 X! c- u
, W, x0 T; H; U; @5 a5 |3 u8 cIf …, then …is said to be …

) o3 T1 t0 F. @) j  \If …, 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
( h( C# ^/ y5 k7 R3 h* A: O1 f0 t& {is called a square matrix.

  B& f- o/ u4 W: R7 ]+ hIf 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：

% o: b/ E/ X- r' b7 x, |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
0 ^  o4 \1 k7 ^: X0 J# ~+ O7 fz1≠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：

Let …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
3 H# e+ ?- a# [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^^