数学专业英语－(a) How to define a mathematical term?

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数学专业英语－(a) How to define a mathematical term? + l) x4 {' d+ c1 w8 u

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数学术语的定义和数学定理的叙述，其基本格式可归纳为似“if…then…”的格式，其他的格式一般地说可视为这一格式的延伸或变形。 * Z* T" D, D q 6 d0 d" S" i k6 p# k6 ^

如果一定语短语或定语从句，以界定被定义的词，所得定义表面上看虽不是“If……then……”的句型，而实际上是用“定语部分”代替了“If”句，因此我们可以把“定语部分”写成If句，从而又回到“If……then……”的句型。 0 j, q' @: o7 L; |$ u! f

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至于下面将要叙述的“Let…if…then”，“Let and assume…, If…then…”等句型，其实质也是基本句型“If……then……”的延伸。

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有时，在定义或定理中，需要附加说明某些成份，我们还可在“if…then…”句中插入如“where…”等的句子，加以延伸（见后面例子）。 % E7 @: W3 x( @* q6 E

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总之，绝大部分（如果不是全部的话）数学术语的定义和定理的叙述均可采用本附录中各种格式之。 - Z, `/ F; p5 b I' k. x; X

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（a）How to define a mathematical term?

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9 R" J p4 n W$ m is defined as 1 Z3 L/ }$ i- M1 }/ V; M # ]9 Z( e8 D" w; K: _2 W7 E" D 9 q1 @! z, J4 Q% I. N( L' l is called

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1. Something something

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The union of A and B is defined as the set of those elements which are in A, in B or in both. 7 z; q; U% j6 M& v# l. v1 v, l5 X

The mapping , ad-bc 0, is called a Mobius transformation.

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is defined to be ; h; }7 `8 Y% A% Q 8 B6 P! s. e1 y5 | N4 ? . q2 T( x0 N& {1 G% B& m is said to be ! s3 s8 c" N! f! a, l( }6 {

2. Something something(or adjective) 8 D- |8 D( P2 p1 J- X

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

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A real number that cannot be expressed as the ratio of two integers is said to be an irrational number. 9 P* C6 z, Q* K* ]/ M# q' C

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Real numbers which are greater than zero are said to be positive. . Y9 \5 E- c6 m, G" J

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define 2 K2 D; G1 N! G. ~, R$ i . `- p1 {" B* B4 `$ B: U7 ~ / ?8 ?) \$ I- W2 O4 I call 6 z# T4 ^) c, p1 }/ \+ h, F8 o6 [ 7 K ]0 [: Z1 R N0 W a7 {7 v* k

3. We something to be something. 3 P, ?, F+ c- [' e! c( q

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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： }( i# |1 R2 r5 H

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5 K+ N& s P6 U4 d" R is called - e* `) R# u9 h0 v m ( f W8 ^1 w$ q, T0 M \ is said to be is defined as & o5 ^2 J/ w7 N% G* s6 e C9 E ( M1 R- e% P0 h! o is defined to be , T9 ~' n& }# v/ t. Y , S# A6 X. t; D9 D) X( W! x% Y

Let…, then… $ A: T8 Y, i e3 C1 V

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Let x=( ) be an n-tuple of real numbers. Then the set of all such n-tuples is defined as the Euclidean n-space R.

Let d(x,y) denote the distance between two points x and y of a set A. Then the number . Q) `* W' N, F3 V% t5 Y! h0 v

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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：

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3 Q0 G% L5 u% G is called 4 _# i% D3 \% [' O0 t is said to be " S8 `8 E* [( _# B% D$ s0 D. I is defined as ; A: S/ w& Q, {6 Z; j is defined to be % f7 R9 r9 ?+ u( G: j5 \9 Q! @

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If…, then…

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If the number of rows of a matrix A equals the number of its columns, then A is called a square matrix.

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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： : N* @ {* _2 k6 k

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3 `& o- D5 }4 P: I! J is called is said to be

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…. If…then… … ! g& d' F7 h" b

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Let f(z) be an analytic function defined on a domain D (前提条件). If for every pair or points , and in D with , we have f( ) f( ) (直接条件)，then f(z) is called a schlicht function or is said to be schlicht in D.

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陈亚玲

棒呆，感谢分享
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2114532685

谢谢啦，还是挺有用处的
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1837154451

谢谢！！！
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1047700174

强，实用
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有、牛

已经学习了，非常有用
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cuise!

发表回复非常实用的句型

有、牛

看后很有感觉
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Donkey^Sunshine

非常感谢你的分享 为我的写作工作提供一定的指导意见
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18833852836

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