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.
6 P( X1 ~  w# P- G  @1 t; N5 iSomething 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.
# W5 [7 b; ^0 x$ s+ {. p2 tSomething is defined to be something (or adjective)

% @: l0 V3 }: d: _! TSomething is said to be something (or adjective)

' A$ y( O* M* Q5 F# i$ D例如：

) s& k' v- D  s$ U3 w1 eThe 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.

' t* [, J3 Z9 b" w( M) U' X( C5 gReal numbers which are greater than zero are said to be positive.

3.
/ V$ B4 c' y. V! d+ O! E6 o2 hWe define something to be something.

# x  x. h* V1 y- ~1 ]% Z  {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.

We 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：

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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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：

9 O) G) ~  F+ k, m- GIf …, then …is called …

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2 p( \$ ?5 c" N! T. a9 C7 pIf …, then …is said to be …

If …, then …is defined as …

4 |2 q' o% t9 R2 |If …, then … is defined to be …

例如：

; q( _" g0 y) \, a  ]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.

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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：

3 W/ l# I+ X$ M. s5 ?: GLet 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
6 @1 o. Q$ G/ k+ j6 Ez1≠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：

) R6 g/ L& X7 x% L% E* b/ C+ [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
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^^