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数学专业英语－(a) How to define a mathematical term?. ^( t' P9 X( B" n" e/ ^
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( B& Z) \! @8 I- k4 z% e- S 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。 5 F: \3 J& b" o$ @% q. r
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# A4 Q z4 t; C8 M- V, `$ l+ n+ |& I% K 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。
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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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, X j' P1 W0 f9 k: t+ \# W# ?' n9 ? 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）。 ; n) e4 A) r8 ]
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! |6 u4 Y$ k b9 E# B6 S 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。 1 O. W d* X0 N; M" S4 i
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0 S2 X7 W9 A8 p' i7 w4 J4 f+ p （a）How to define a mathematical term?2 g* y0 h; j7 H+ R6 T7 }$ Q0 e: i
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4 E" W% B% D1 ~2 C* } is defined as
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is called
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1. Something something
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( ]8 U% s' a& H8 G ^+ [/ C( u 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. 4 L7 K" W- M& ]$ O% v
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is defined to be
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4 g$ f" _* y$ Q$ T is said to be
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' `+ j( e, B3 X: U2. Something something(or adjective) - }& C1 Q* D& Y) g! U0 D
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# Y( G7 W% o" C 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.
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Real numbers which are greater than zero are said to be positive. ; h# I: n- ]6 l; k# a: J3 ~
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3. We something to be something. 7 a* N+ S: g% @8 L
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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. 4 d+ Q) f5 k1 b; r; U, X; d
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We call real numbers that are less than zero (to be) negative numbers. - W' l" a2 v! z8 N5 B
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1 r4 i$ m3 @/ a# {8 Y- m 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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4 [6 x$ t; X& R# U+ g) \) G is called
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8 g1 g1 U4 s4 F! v, [; V is defined as
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Let…, then…
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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. 8 b& N. a) ?$ b, j' W) W
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4 ~2 l: [! T% V Let d(x,y) denote the distance between two points x and y of a set A. Then the number ' {4 a6 m v: D' U9 P) [
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is called the diameter of A. , N. ~+ G: N# o% u0 b& I- P( t
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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： $ E z1 f) q& u# R: ]+ r4 Y7 v
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8 }+ j! {* E: \! j- E/ j is called . [# z/ C; {. p; Y! S7 S
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is said to be 9 a) ] e& b( V' O! b
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0 H9 N1 `5 x8 F: U6 W: D is defined as
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0 @2 E; J {7 N. z If…, then… , ]' x6 \: o4 ]8 z0 y
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7 ^8 l6 u& z/ d, x3 x X5 J% [" h' _7 y If the number of rows of a matrix A equals the number of its columns, then A is called a square matrix. $ D; I I8 j. x P( t6 p, C# E
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5 d. Y& N- I1 M If a function f is differentiable at every point of a domain D, then it is said to be analytic in D. ; r/ I& f; x$ P1 k$ u
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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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4 {! c# Y/ D2 x9 ~4 n+ I( a# Zis called 9 J" w$ G# F( r* m
is said to be |
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Suppose | …. If…then… … # D2 q5 ~8 g y! ~
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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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