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.

Something is called something.

3 N  J1 |8 g. Y- X5 p  ]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.
8 ?1 ^# [6 f# x3 g& ~  U& A+ hSomething is defined to be something (or adjective)

/ @: Q  G1 C5 eSomething is said to be something (or adjective)

( b0 |, B: S& X0 f, r+ D7 r例如：

0 j  \( Z; H  g( [( V( r0 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.

% Y$ }, E) p8 R$ FReal numbers which are greater than zero are said to be positive.

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3.
0 u9 b! X6 X( b  f" gWe define something to be something.

  Q) ?2 m) f+ ?' |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.

" b6 y  |$ N0 l: q. |We call real numbers that are less than zero to be negative numbers.

4.
' B- g6 {3 X0 p: q' V" q& Y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 …

+ n. q# l$ y5 v4 KLet…, 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.

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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：

If …, then …is called …

$ U  z9 Z& S5 @  }% G7 v4 G- @9 [7 JIf …, then …is said to be …

If …, then …is defined as …

If …, then … is defined to be …

例如：

' h7 y* G/ {8 H& O6 p/ d* Y7 XIf 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：

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
0 G  G; {8 m8 D& O7 @0 M$ \2 w0 j3 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.

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：

! x  V# v1 n9 l; k* E  u2 sLet …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
z1≠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^^