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数学专业英语－(a) How to define a mathematical term?0 m" R7 Z" f0 q
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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。 & t. ~" n# T( O* _( h+ p2 Z- A
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; d; ?* A+ Y" v8 k! O5 l) x 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。 + p$ X& T, C. Z* N
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! B4 S+ {% B: o/ h% f 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 w7 W3 X! k5 a' T+ L* o
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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）。 + A* r8 h* H: D( V
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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。 ! A. ~7 ]: Y, \1 P& J" q4 q9 S
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8 k$ J9 I/ t4 u* p （a）How to define a mathematical term?
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is defined as
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is called # \" h- P( H6 E- z+ s0 b; r. i6 m' j$ N5 s
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0 f* k, S9 n; M7 }) a# h" h1. Something something
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# h, N2 R, I1 l9 T' v3 N 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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1 z0 K1 p' ]7 j2 n! p; t is defined to be 5 ^( c, f; s* t- Q8 F
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is said to be
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2. Something something(or adjective)
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9 z+ X2 o( {4 L9 u- P# T l The difference A-B is defined to be the set of all elements of A which are not in B. ! `" s" ^( r4 R( t0 Q- K
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A real number that cannot be expressed as the ratio of two integers is said to be an irrational number. + V6 Y4 K; k7 B% g+ l
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4 u$ S, R8 j1 l' | Real numbers which are greater than zero are said to be positive. ; z4 t# F$ B# p7 c5 l0 Q- r
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% l# \" H6 A1 O9 ?: E. M define ( r4 Z& r1 i0 @) U& o
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" l; U: _7 x- `3. We something to be something. 0 \9 n: I$ u$ F
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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. # | t% h$ S8 v$ d% B' w4 E
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( z: Q z3 ^+ s& @; Z" f5 J We call real numbers that are less than zero (to be) negative numbers. % h# \& o% t; G, 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： 2 h' ]: \) n2 r
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is called
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is said to be : ?- W' r r5 I
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is defined as & Z' @* b* F' W P o
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is defined to be
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. p; J. |& X8 W6 J Let…, then… & a/ S* f- ~ F0 e3 q
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; ~- X. Y. I; j, F0 a) O/ i! [ 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.
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4 R2 `2 T" S# s Let d(x,y) denote the distance between two points x and y of a set A. Then the number
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4 |8 D8 P, M7 B% r+ Q4 ]. Z/ { is called the diameter of A.
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" a( E! P+ e' _! ~ 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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4 T! ^& M' @! O i6 {3 T& b is called - R+ `' T# |% C0 W! _, O
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If…, then…
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3 E9 D1 S! L: g6 Z+ }6 ~" u1 j 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： t2 H8 h) L4 T. _, ?
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7 ?: R& P/ g4 x- V9 ]* xis called : |$ r8 j4 ]5 H0 a* ]3 r
is said to be | 3 N- p" U, N4 z. H( `% G
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Let ) f: S4 [0 F& i. L- {- @& ~3 d
Suppose | …. If…then… …
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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. - L* R2 P5 e8 D9 ^' N
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