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.
) h) M* d  ~6 `' G5 Z: _/ A1 `- OSomething is defined as something.

/ c+ L* q  [, OSomething is called something.

: k  o; A5 ?$ v* ^$ T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.

. R) r0 ~1 ~/ _% t5 DThe mapping ,is called a Mobius transformation.

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

Something is said to be something (or adjective)

例如：

, o, M4 R" [  X) \" ?% P: c* jThe difference A-B is defined to be the set of all elements of A which are not in B.

) M: S7 T6 ?8 d9 A- E( m. pA real number that cannot be expressed as the ratio of two integers is said to be an irrational number.

8 L- K& ?& u  W& K1 l+ s# u# GReal numbers which are greater than zero are said to be positive.

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3.
We define something to be something.

4 k! ?) c- c. ^: o4 g7 `. Z& vWe 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：

% y7 h; Q) @, y* @- {Let…, Then … is called …

5 Y5 e8 L4 ?2 h( R# d, D! nLet…, 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

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：

/ \6 m" h# w; O  @% _9 qIf …, then …is called …

4 K- W' m( L! ?$ s, O( f2 O: n3 OIf …, then …is said to be …

If …, then …is defined as …

If …, then … is defined to be …

例如：

) Z7 P% U) Y% D0 Y) FIf the number of rows of a matrix A equals the number of its columns, then A
6 u' j/ o& V2 p, T# g& m0 _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：

1 f0 W  t9 H0 U/ B7 D, SLet(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：

) k( z, ~% R2 s$ a" M6 T/ I) ELet …and suppose(or assume) …. If … then…is called…

例如：

7 q. Q. |, {0 zLet 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^^