→ bineapple :e(1+2a)=0要對所有的有理數a成立 所以只有0這個選澤 11/10 09:53
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？
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