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独孤九剑

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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 |正序浏览
    |招呼Ta 关注Ta
    Group
    : u4 P/ k" i. g- P' X  T2 NA group is defined as a finite or infinite set of Operands
    ( B# T2 v, [( F" ] (called ``elements'') , , , ... that may be combined or ``multiplied'' via a Binary Operator. K/ R% c7 V/ `5 v# t* S
    to form well-defined products and which furthermore satisfy the following conditions: ! a, E& j9 t$ B
    1. Closure: If and are two elements in , then the product is also in .
    3 K  I* F- a4 Y8 s2. Associativity: The defined multiplication is associative, i.e., for all , .
    + _  g4 |- K. ^3. Identity: There is an Identity Element
    : C* ?) b# d2 N1 O, A8 Q2 b4 ^0 J# g (a.k.a. , , or ) such that for every element .
    . Q* }* F# ?% k1 g$ ^: w. N4. Inverse: There must be an inverse or reciprocal of each element. Therefore, the set must contain an element such that for each element of . 7 |( f+ Z3 K& s. R/ G0 K
    A group is therefore a Monoid& I" i: _. p1 U, w- c+ W
    for which every element is invertible. A group must contain at least one element. . _  s! X$ @9 ^: ?9 Q( t7 A5 Q0 ~
    + N1 O8 ~7 y( ^
    The study of groups is known as Group Theory
    1 s. K1 ~7 y. ?7 V. n3 ]/ d" g% r. If there are a finite number of elements, the group is called a Finite Group
    7 z3 v0 V3 `- S7 } and the number of elements is called the Order
    . Q1 I( r& \5 W( d+ p* \ of the group.
    1 }8 I  {. O4 k; j$ s. v6 p ' |. d% h$ \% ]! n0 S, r
    Since each element , , , ..., , and is a member of the group, group property 1 requires that the product
    4 w: ]$ s4 m4 |' I- p( ^% M

    7 U! e! r/ x: }
    (1); h5 T+ c0 T1 Q' }& m

    ) ?* Q/ L7 D" m1 v2 d# h$ ?4 S, }$ s2 r" E

    : v; X+ W# u+ d4 q. ?: Zmust also be a member. Now apply to ,
    / k2 |7 p! k0 R8 H9 {$ a' R- l
    2 m& ?1 O# B8 {
    + q, i  C7 Y% a0 Y9 T
    (2)% T7 p  c6 |' S- R" ~! Q
    - n, N% }% d1 A" C8 A; n
    9 D+ `/ L8 V6 ^2 F
    6 B4 f  \6 V- g
    But ; v/ ^3 f) V, X5 b0 y5 C3 P" x

    8 o# v- ?! D2 `5 g& l
    8 \( [$ ~4 ]' c' W

    4 e: I  u; t6 @; t5 [$ \
    & L  @% R: F' Q& e. D/ f* M' n

    1 C4 W6 L1 W) g" B# D( y
    (3)
    " a3 w8 D+ x# t7 P" O$ z/ B+ v& t, A8 A
    so 6 _5 k0 j8 s( e  O$ x% X' T

    # x* l  V& w/ l
    (4)
    9 z& X6 u3 k6 l( ?8 o

    + h* q/ u/ b$ b* t9 T1 Y( w7 {: f) _2 g. B. p" L8 i

    / R3 h$ z+ w4 j/ c9 x! K* b! Dwhich means that
    / _7 ]. U$ R) s( b# r/ _

    / x& t9 O$ y  x. K1 B
    (5); u. f* U+ x3 `3 A+ Q: \
    & n# [! J& o  C% \' V- h6 h
    ! [' C1 Y1 \( x
    : L$ C. `, l  ~* Q% P/ u
    and
    0 |' \! b# M6 W0 G

      A1 Q6 v& b) j1 T
    (6)
    1 ?4 _  r+ ?2 y

    ; h( J- p: E) F* n5 J# H; R2 |; y: w3 h) ]9 \

    ! Y0 u9 e7 }8 Q8 Z. G9 o
    8 M3 K: T" o* b2 ~& K7 }- S+ ~; |( D# `( r
    zan
    转播转播0 分享淘帖0 分享分享0 收藏收藏0 支持支持0 反对反对0 微信微信
    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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