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.
9 D" u  ?! ]+ \% BSomething 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.

( i' R6 [2 \, Y7 p& R1 fThe mapping ,is called a Mobius transformation.

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2.
& T2 k+ f& I$ B' rSomething is defined to be something (or adjective)

Something is said to be something (or adjective)

- X6 A! t* t4 H% B, e* L: l例如：

The 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.

; R  d5 f# ^) \+ E) L/ f& Y9 I) V% t$ PReal numbers which are greater than zero are said to be positive.

3.
We define something to be something.

- X' P8 x% d$ AWe 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.

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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 …

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 .

9 i' u0 ^5 L0 Z! |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：

. i9 e+ m8 a! j) SIf …, then …is called …

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If …, then …is said to be …

If …, then …is defined as …

# J1 `- _/ \9 c/ z9 lIf …, 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.

! v% [* `% G7 vIf 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：

8 i% A/ d) q/ E, I( D& \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
1 B4 I# v% V2 g6 qz1≠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.

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：

; d4 @% z* x% i0 E( P/ Y0 yLet …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
1 u8 `: D' z% W" P% P6 c: S1 |8 Qz1≠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^^