Re: [代數] 兩個有關group的問題

看板Math作者star66 (star)時間13年前 (2012/11/10 09:35)推噓0(0推 0噓 1→)

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我看了這題有一個疑問.... : : 1. Let * be the binary operation on the rational numbers is given by : : a*b=a+b+2ab. Which of the following are true? : : (A) * is commutative : : (B) There is a rational number that is a *-identity : : (C) Every rational number has a *-inverse. : : Ans: A,B : 在(Q,*)當中: : Given a belongs to Q : a*e = a+e+2ae = a (by def.) : => e(1+2a)=0 => e = 0 (這就是*的identity) 為什麼e(1+2a)=0就能推到e=0？且e=0就是*的identity? 是兩邊同乘(1+2a)的反元素嗎？那萬一a=-1/2的話怎麼辦？ -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 173.10.139.205

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11/10 09:53, , 1^F

11/10 09:53, 1^F

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