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.
+ r% A4 f8 V0 s, b3 u& eSomething is defined as something.

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

Something is said to be something (or adjective)

1 v/ Z% q3 O! S5 b$ ]6 y" ^例如：

; j! _8 p( E) lThe 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.

& O5 w4 j" W* J0 A" fReal numbers which are greater than zero are said to be positive.

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3.
5 u6 x. w. W5 Z$ F/ p6 x9 S/ sWe define something to be something.

  s; M  l2 L5 }2 N. A+ j* E. ~We 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.

6 \1 o3 f$ W3 ZWe call real numbers that are less than zero to be negative numbers.

4.
4 o0 @* H0 }* g1 O, n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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; X. u. m  K% o5 X, jLet 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：

- Q0 D% R/ @0 m# q% D% P  |* WIf …, then …is called …

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If …, then …is said to be …

) k6 i) W4 ^2 Z0 bIf …, 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
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.

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：

) h0 v4 {# J- Y# e# J/ b  i5 cLet(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
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：

- ]/ k5 O4 d- U; HLet …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
" o; L* M( @" K$ bz1≠z2 ，we have f(z1)≠f(z2)，then f(z) is called a schlicht function .

许凡

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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^^