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    郁闷
    2012-4-30 23:06
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      “独孤九剑”的要旨,在于一眼见到对方招式中的破绽,便即乘虚而入,后发先至,一招制胜,

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    1#
    发表于 2009-2-2 22:25 |只看该作者 |倒序浏览
    |招呼Ta 关注Ta
    Group " ]# A( P0 @1 m/ x  n' G
    A group is defined as a finite or infinite set of Operands. d$ w# L6 k* C! A
    (called ``elements'') , , , ... that may be combined or ``multiplied'' via a Binary Operator  l: J. J! ^4 k8 H& l. J
    to form well-defined products and which furthermore satisfy the following conditions:
    4 I# D% N, t; E7 s% g* D* i+ @1. Closure: If and are two elements in , then the product is also in . 4 V$ X0 s  u3 U1 j
    2. Associativity: The defined multiplication is associative, i.e., for all , .
    3 n; e7 `2 @  ^9 m' `3 B  b2 T3. Identity: There is an Identity Element0 W: h' E  |6 I% }. `' P/ @! P
    (a.k.a. , , or ) such that for every element .   K1 U8 |: h5 [1 f  ^* u) _
    4. Inverse: There must be an inverse or reciprocal of each element. Therefore, the set must contain an element such that for each element of . $ M# e& ?  G6 `! Z5 o$ G. V
    A group is therefore a Monoid
    & f& t) g: {  i/ l. x/ ~* A5 g1 x for which every element is invertible. A group must contain at least one element. 4 z9 h4 P: j* ]" |5 c& @: P

    + ~2 L1 D, F1 r* t7 pThe study of groups is known as Group Theory$ n! z- e# E+ G
    . If there are a finite number of elements, the group is called a Finite Group; `, |; {+ i) F: l) s( ?9 d7 `
    and the number of elements is called the Order$ E7 r# u+ X7 v! |$ S* z5 l( p
    of the group.
    # |7 ]: ]/ X( M) Z# a " L- a6 n/ c/ x- d
    Since each element , , , ..., , and is a member of the group, group property 1 requires that the product
    # }- b  r8 M+ y0 E5 S

    ' P) K& l9 x& z8 p7 b  h
    (1)
    # v/ X" u) f; R' _
    1 @& E6 g+ h. x& _1 \' Q
    1 M1 F- S- d( {3 E6 d/ k

    ) t* P( Z) F7 c+ C% Fmust also be a member. Now apply to , 2 M( m: s4 P5 p( `
    . r. l* x- q  D% z3 R5 Q2 ?

    % {) A% P  f! w: g% p
    (2)
    9 C7 R" |8 G$ n, }" N6 p

    3 L9 t6 B/ C5 A- T# J
    7 E1 Y9 [3 a5 k* D# {) X; Z
    6 P# Y0 x: d1 uBut 0 w$ G5 H4 X+ C4 M, s  z
    8 W& C- I7 _. a
    0 j; f. @6 u& Y
    & h4 s, V2 f  t, }/ l
    8 u$ G  k% g5 R2 l( v$ f

    6 R3 s+ l4 ~# h  y5 E( `: I
    (3)1 k; X. M9 _! b7 A5 Q4 h4 W
    so
    5 n) J7 f0 a, R) ^6 h: P

    5 w% t# \! S/ {, ~# w
    (4)
    , }8 i# u- ~9 Y7 L: v
    # x! b4 e  @7 d4 V% z) b& g

    ) z" C0 ^' g. |% D0 L& k. E. g" V/ w1 p+ i/ R3 b* B& Y- ]. e
    which means that
    & R4 r3 q. @! [+ r
    5 {( q6 r  ]* W5 m, ]
    (5); ^2 S: `4 p# p2 o  }$ s
    % q: r6 B( w4 z0 e- {

    " j& `, b* _9 f
    ( j3 |/ p; G: {: b2 C/ E" ]and
    ( Y, n: g( m  ?6 u9 i

    + V' n2 \# t0 q- ~5 A, S( h
    (6): D$ _- C' T9 S; e8 O( _7 x" E

    . N$ U6 i6 b( F* i: X3 p0 v
    6 ?( ~7 Y2 _+ Z* G3 @
    ; E, x8 o4 w- q' ^6 h # e) T7 f, B3 c! q
    7 _% t- w! I- Z; T1 j. M, C
    zan
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    OLS 实名认证       

    60

    主题

    6

    听众

    1594

    积分

    独孤九剑

    升级  59.4%

  • TA的每日心情
    郁闷
    2012-4-30 23:06
  • 签到天数: 6 天

    [LV.2]偶尔看看I

    自我介绍


      “独孤九剑”的要旨,在于一眼见到对方招式中的破绽,便即乘虚而入,后发先至,一招制胜,

    新人进步奖

    群组南京邮电大学数模协会

    群组数学散仙

    群组数模应用

    群组数学趣味、游戏、IQ等

    群组2011年第一期数学建模

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