(How to define a mathematical term?)
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) D9 d# e2 ]8 z: X$ x' SSomething is defined as something. : s. h6 [1 Y# H4 x3 M" ^2 x2 @
Something is called something.
/ D0 i& x8 U- |* ?2 A# O% O) S例如:
The union of A and B is defined as the set of those elements which are in A, in B or in both.
& M+ v: l, x$ u+ m# ]# pThe mapping ,is called a Mobius transformation.
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) e N7 N; S4 M% Z8 _' VSomething is defined to be something (or adjective) 4 k8 X( m' b: c; w! D }
Something is said to be something (or adjective)
5 v) T) k" o' Z% r3 f; S$ }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. & ^) @: e7 o7 Q: m8 L% V" W
Real numbers which are greater than zero are said to be positive. 3.
7 x& y m; p2 k Q; v; h8 [We define something to be something. 0 v! F; _; B+ }8 t7 ^$ | s) U0 F) R
We call something to be something. We define the intersection of A and B to be the set of those elements common to both A and B.
" r T' _6 i/ n4 M6 s' QWe call real numbers that are less than zero to be negative numbers.
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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:
' b7 _, p. O+ A( K- s$ XLet…, Then … is called …
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Let…, Then … is said to be … Let…, Then … is defined as … Let…, Then … is defined to be … Let x=(x1, x2, … xn) be an n-tuple of real numbers. Then the set of all such n-tuples is defined as the Euclidean n-space Rn .
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Let d(x,y) denote the distance between two points x and y of a set A. Then the number is called the diameter of A. 5. 如果被定义术语,需要满足某些条件,则可用如下形式: + D& ~1 U! h# ^0 e/ d
If …, then …is called …
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If …, then …is said to be …
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If …, then …is defined as … ) \! d9 Q D5 q2 a/ J
If …, then … is defined to be …
. H7 V% @+ r3 t# |1 I, gIf the number of rows of a matrix A equals the number of its columns, then A7 `! w5 p) {: z! p+ ?
is called a square matrix.
- c- I/ W5 ]+ K) L( OIf a function f is differentiable at every point of a domain D, then it is said to be analytic in D.
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: ( G" g1 d% X' e5 R" k* @
Let(or Suppose) …. If …, then … is called … Let(or Suppose) …. If …, then … is said to be … ; S1 ^/ d M, ?. b- w
Let f(z) be an analytic function defined on a domain D(前提条件).If for every pair of points z1 and z2 in D with
0 y% M Y( A9 p4 Mz1≠z2 ,we have f(z1)≠f(z2) (直接条件),then f(z) is called a schlicht function or is said to be schlicht in D. 7. 如果被定义术语需要满足几个条件(大前提,小前提,直接条件),则可用如下形式:
8 y: V. ?& M/ u# ^5 TLet …and suppose(or assume) …. If … then…is called…
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Let D be a domain and suppose that f(z) is analytic in D. If for every pair of points z1 and z2 in D with
% w1 u" k+ }! X* B+ F) Jz1≠z2 ,we have f(z1)≠f(z2),then f(z) is called a schlicht function . |