作者:
yueayase (scrya)
2020-11-19 23:15:14※ 引述《Gikber (Gikber)》之銘言：
: 大家都知道1乘以任何數字都會等於被乘數
: 而0被任何數字乘就會等於0
: 這數學界兩個最強的矛與盾碰在一起時
: 到底是因為1乘以0所以等於0
: 還是因為0被1乘了所以等於0呢？
: 有沒有卦？
https://mathworld.wolfram.com/FieldAxioms.html
By field axiom, for all x in F,
0x = 0x+0 (by identity for addition)
= 0x+[0x+(-0x)] (by addition inverse)
= (0x+0x)+(-0x) (by associativity)
= (0+0)x+(-0x) (by distributivity for multiplication)
= 0x+(-0x) (by identity for addition)
= 0 (by addition inverse)
0x = x0 (by commutativity for multiplication)
所以1*0=0*1=0