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.

/ X1 i- @* o( W+ `7 ^/ l- KSomething 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.

8 w# p" i1 K1 B1 y7 r% jThe mapping ,is called a Mobius transformation.

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

  K  f% P: q8 p$ Y. ZSomething is said to be something (or adjective)

例如：

The difference A-B is defined to be the set of all elements of A which are not in B.

# }5 M0 \: U" k+ a3 X! GA real number that cannot be expressed as the ratio of two integers is said to be an irrational number.

" i9 N1 ^# z+ HReal numbers which are greater than zero are said to be positive.

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3.
We define something to be something.

We call something to be something.

3 {5 G6 o4 a0 R' R例如：

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

% v4 h; j% u, ~* @  T0 PWe call real numbers that are less than zero to be negative numbers.

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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 …

) E! H: v1 N4 p3 Y/ v. q  GLet…, 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 .

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.

5. 如果被定义术语，需要满足某些条件，则可用如下形式：

If …, then …is called …

If …, then …is said to be …

If …, then …is defined as …

If …, then … is defined to be …

例如：

/ D  M* B" V0 A% a3 c4 |# f5 pIf 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：

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：

7 ?! _3 {! p: x  wLet …and suppose(or assume) …. If … then…is called…

例如：

4 _# a$ P! T. I5 oLet 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 .

KaloDark

楼主找的就是你^^

凸眼金鱼

分享了~~~~

joyce19880122

太好了，不用花钱。谢谢谢谢～

zwt1987

好东西哦，分享了啊

zhenghui999

henhao    henqiang da

许凡

还有没有更多的啊