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? 1 b0 v8 L9 h4 I/ w. x + k: a1 F' C" k

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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。

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。 7 J; |+ O; D2 l$ l" l( S8 @8 p: M

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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。 5 z7 _! i# M6 g

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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）。 ' {. h9 q) {5 s' j. G" s

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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。

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（a）How to define a mathematical term?

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+ w0 q1 R5 K1 d: t( o6 F is defined as / B+ O! C- I) a8 p : N/ r* U# u2 F$ I% C" J; W; t 8 c. X8 m! x& z* j% I4 F is called # D" t! j" t7 U' S/ h7 Z) `+ ^

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1. Something something ) f4 D5 a9 o' R* g; Q: D% _6 v, G

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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.

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

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- u9 [( \$ ?2 ^/ r% K+ V' ` is defined to be is said to be

2. Something something(or adjective)

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The difference A-B is defined to be the set of all elements of A which are not in B. 4 }' M/ N5 ?" x

A real number that cannot be expressed as the ratio of two integers is said to be an irrational number.

Real numbers which are greater than zero are said to be positive.

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+ h2 r+ k# u4 J define ' E, n) u! R2 }& v3 o; t ' e% i/ \! G6 ?" h6 Q call 6 s2 ^! N x' i3 L! T % g7 J5 Y0 F* X7 W

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3. We something to be something.

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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.

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We call real numbers that are less than zero (to be) negative numbers. ) h" Z( {# R. j' ?7 q

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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：

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" X! ~. L. K2 ~8 R1 _5 | is called 8 _- I$ K! Q3 {, |) C! z A+ E 9 [9 ]4 {' n+ p6 H/ g/ ^/ R0 b is said to be 9 g0 z( n' r9 N6 t. ] is defined as ( N: N+ W: u; p- g! U3 b is defined to be " [8 |+ S6 W9 r9 D6 ~8 K

Let…, then… & \4 `0 S. z# o& h* Y4 W

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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. 7 k6 p" `0 h0 P- H5 h& q1 r2 h7 L

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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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D=

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is called the diameter of A. 7 d% t, D" u- F' @, `* @/ a+ y

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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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* }" G2 K; ]- {, s5 r v) d* K3 w! j is called + p7 @+ I5 ~) N' l2 Y is said to be 6 ]+ d# P |9 y is defined as 5 T) Z) x# e: ]2 V" I/ } is defined to be & N, q/ }% F4 v

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. ) a( i, T3 n5 ]( _8 J' a" X

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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：

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* E4 E$ a$ z0 C; ^. d0 r7 r, V is called , {$ p6 _4 _2 ?& w) |4 }- I is said to be

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1 j6 ?) ^7 h; y Let Suppose

…. If…then… … 2 S2 s {" _/ i

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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

1837154451

谢谢！！！

1047700174

强，实用

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
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有、牛

看后很有感觉

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

18833852836

发表回复顶一下
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