数学建模社区-数学中国

标题: 如何定义数学用语 [打印本页]
作者: kidd0323    时间: 2009-2-5 10:44
标题: 如何定义数学用语
如何定义数学术语?
（How to define a mathematical term?）% s" U( ~/ T3 K2 K, R6 F, I

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1.
( q6 F% F* Y, ?% e# f8 ?5 P! }Something is defined as something.

0 U$ J5 B3 J9 F4 k( x' QSomething is called something.

& B9 W! P( I* q! w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.
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The mapping ,is called a Mobius transformation.

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2.
6 Z8 d- i7 o# TSomething is defined to be something (or adjective)
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Something is said to be something (or adjective)

9 s* k+ T7 i# r& }1 ]例如：
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The difference A-B is defined to be the set of all elements of A which are not in B.

9 d+ E! r1 E) ?* _, P1 V/ n+ WA real number that cannot be expressed as the ratio of two integers is said to be an irrational number.

+ ]. V2 C1 Z5 L! c/ U! LReal numbers which are greater than zero are said to be positive.
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We define something to be something.

4 m% |; J2 |2 U, A; q2 Q0 YWe call something to be something.
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例如：
We define the intersection of A and B to be the set of those elements common to both A and B.

1 O3 s5 r& r# w( o2 V9 t( cWe call real numbers that are less than zero to be negative numbers.

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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：

5 Q  K" L8 }& N, W! gLet…, Then … is called …

8 R3 i% r# p! k: ILet…, 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 .4 u3 t5 a5 O4 ^
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Let 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.

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5. 如果被定义术语，需要满足某些条件，则可用如下形式：
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If …, then …is called …
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' i1 x* i5 X) f% pIf …, then …is said to be …

0 E; T( N3 F# }/ d% T: ]5 J$ RIf …, then …is defined as …

: i4 b* b2 c6 a; M% I/ C) d. i; BIf …, then … is defined to be …
例如：

/ U4 I0 p; J4 d6 zIf the number of rows of a matrix A equals the number of its columns, then A$ `7 }1 d1 i4 X# `
is called a square matrix.

8 k* Q+ v9 p% N+ b& oIf 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：

  I2 f6 I5 r8 f4 }" LLet(or Suppose) …. If …, then … is called …
Let(or Suppose) …. If …, then … is said to be …
例如：
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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
, I: I$ {2 O& J$ Rz1≠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：
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Let …and suppose(or assume) …. If … then…is called…
例如：
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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# ?+ D( I5 @3 ~( G5 h. e3 F/ z
z1≠z2 ，we have f(z1)≠f(z2)，then f(z) is called a schlicht function .
作者: 许凡    时间: 2009-2-5 10:49
还有没有更多的啊
作者: zhenghui999    时间: 2009-2-5 11:16
henhao    henqiang da
作者: zwt1987    时间: 2009-2-5 16:48
好东西哦，分享了啊
作者: joyce19880122    时间: 2009-2-7 22:12
太好了，不用花钱。谢谢谢谢～
作者: 凸眼金鱼    时间: 2012-2-6 22:36
分享了~~~~
作者: KaloDark    时间: 2013-1-21 22:43
楼主找的就是你^^



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