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?）$ K% _1 S3 r( S& }

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1.
& O3 H2 a4 P& t2 J6 p6 X) s% ^Something is defined as something.
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Something is called something.

3 p  n9 g* J( P, F% z% L2 e5 |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.

- ~) C+ S- [! @( {0 _The mapping ,is called a Mobius transformation.

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2.
9 d- l) k( M- XSomething is defined to be something (or adjective)
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Something is said to be something (or adjective)
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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.

1 S# u* i/ b8 d3 O$ ]A real number that cannot be expressed as the ratio of two integers is said to be an irrational number.

( k: k0 V3 |) j7 N  _3 F# ?2 EReal numbers which are greater than zero are said to be positive.

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3.
0 L- z6 b2 R% j  k4 k- r4 U: O  SWe define something to be something.
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We call something to be something.

/ g8 c1 E" U/ f5 h- _5 k+ g' }, g例如：
We define the intersection of A and B to be the set of those elements common to both A and B.

. ]/ {+ K0 ^$ s1 Q/ W. J; FWe call real numbers that are less than zero to be negative numbers.
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4.
8 K; b  p1 H# Z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：
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Let…, Then … is called …
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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 .8 w: Z: A. P! q/ d4 D' R, c0 W
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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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If …, then …is said to be …

( D9 c+ L! j. g) ?If …, then …is defined as …
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If …, then … is defined to be …
例如：

, R7 r7 y6 v/ [4 g& ~5 \0 v; bIf the number of rows of a matrix A equals the number of its columns, then A
/ R' q8 r5 G' O( {1 n% b3 Q1 Ris called a square matrix.

: T; T1 J6 a" \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：
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Let(or Suppose) …. If …, then … is called …
Let(or Suppose) …. If …, then … is said to be …
例如：

' Y$ a2 D% W- h- W4 U$ h) `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, n9 X5 s! J4 {, i; ~
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.
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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：

. g! W$ X* _/ U( \4 ULet 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. s% N) V+ o2 `1 b# O
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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