Re: [問卦] 為什麼負負得正？

使用環論 整數環 利用 封閉性 單位元素 反元素 分配律 交換律 大概是代數二的範圍 一般當做習題 by ring thm in Z -1 is the inverse element of 1 such that 1+(-1)=0 by closure -1*-1 exist in Z suppose -1*-1=a a=-1*-1 =(0+(-1))*-1 =(1+(-1)+(-1))*-1 by distributive law =(1*-1)+(-1*-1)+(-1*-1) since 1 is identity of * =-1+a+a we have a=-1+a+a since a in Z, -a exists and in Z => -a+a=-a+(-1)+a+a by comutative => 0=-1+a => a is the inverse emelent of -1 =>a=1 so we got -1*-1=1 for m n in Z -m is the inverse element of m -1*m+m=(-1+1)*m=0 we have -1*m is also the inverse element of m so -1*m=-m generally since <Z,*> is commutative -m*-n=-1*-1*m*n=1*m*n=m*n Q.E.D -- Sent from nPTT on my iPhone XR -- ※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 42.74.46.50 (臺灣) ※ 文章網址: https://www.ptt.cc/bbs/Gossiping/M.1683643428.A.6E3.html