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数学专业英语-(a) How to define a mathematical term?
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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。
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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。 9 M2 H' @# t/ C2 k
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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。 - F* g m7 ?6 V/ Z1 X
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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)。 e$ C( I& k) ?& s' N8 x+ c
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$ ?4 d$ H) ?1 b; n# u5 s/ [0 e' k 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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is defined as
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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. 6 K+ \$ j- [! p* P
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6 y+ E% D" _$ m The mapping , ad-bc 0, is called a Mobius transformation. ' E7 N9 s4 V" |0 z9 z7 b
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is said to be
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5 M$ W3 j! _+ d0 D0 r2. Something something(or adjective) 1 g3 p2 E7 c/ X6 A" I0 p! g% I
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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.
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5 a+ S8 v( g; v) F: M, D/ i* e/ P1 O Real numbers which are greater than zero are said to be positive.
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define ' |- |" G" g9 G( x
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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. 2 ?; H5 }( i. G1 e8 i3 ?! H5 Q( O
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We call real numbers that are less than zero (to be) negative numbers. ; f* _1 y: f) D& x1 y5 x+ f0 ^
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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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is called
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is said to be 6 G7 W' F1 K2 z0 o
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is defined to be
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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. 3 u) d: n: n4 O) w9 {. o p5 Q; k) }
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6 @* `. X! g8 h f Let d(x,y) denote the distance between two points x and y of a set A. Then the number . x! L" Q4 G- j0 p- w$ y+ ^6 _; g
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D=
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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: 8 }% _) B) N& z, C" T, K6 d7 Y
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is defined to be
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If…, then… ( p: r3 g4 }4 ]8 [" ^
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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. 2 s0 i+ r' T Z& e, {& B9 e
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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: + {( m, [% M! w7 j
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is said to be |
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Suppose | …. If…then… … 4 D+ G4 |$ C, ?) ?- ~ `1 B
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* n# a6 K, }% ~3 V, z 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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