由 gkw0824usa 於 星期日 四月 08, 2007 12:10 pm
#ed_op#DIV#ed_cl#我發現一個很奇怪的現象,不知道是不是我算錯了:#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#FONT style="BACKGROUND-COLOR: #40ffff"#ed_cl#1. Let f(x)=x+1,#ed_op#/FONT#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#FONT style="BACKGROUND-COLOR: #40ffff"#ed_cl#initial multinomial#ed_op#/FONT#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#FONT style="BACKGROUND-COLOR: #40ffff"#ed_cl#→ f(x+1) =x#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#+1-2(x+1)-1#ed_op#/FONT#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#FONT style="BACKGROUND-COLOR: #40ffff"#ed_cl#Let x=-1,#ed_op#/FONT#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#FONT style="BACKGROUND-COLOR: #40ffff"#ed_cl#f(0)=1 #ed_op#/FONT#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#FONT style="BACKGROUND-COLOR: #40ffff"#ed_cl#→ f(x)=x+1 holds .......(1)#ed_op#/FONT#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#FONT style="BACKGROUND-COLOR: #ffff80"#ed_cl#comparism:#ed_op#/FONT#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#FONT style="BACKGROUND-COLOR: #ffff80"#ed_cl##ed_op#/FONT#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#FONT style="BACKGROUND-COLOR: #ffff80"#ed_cl#Let f(x)=f(0),#ed_op#/FONT#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#FONT style="BACKGROUND-COLOR: #ffff80"#ed_cl##ed_op#/FONT#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#FONT style="BACKGROUND-COLOR: #ffff80"#ed_cl#initial multinomial#ed_op#/FONT#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#FONT style="BACKGROUND-COLOR: #ffff80"#ed_cl#→ f(f(0))=f(0#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#)-2f(0)-1#ed_op#/FONT#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#FONT style="BACKGROUND-COLOR: #ffff80"#ed_cl#→ f(1)=1-2-1#ed_op#/FONT#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#FONT style="BACKGROUND-COLOR: #ffff80"#ed_cl#→ f(1)=-2........(2)#ed_op#/FONT#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#paradox:#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#let x=1,#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#In (1): f(1) = 2#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#In (2): f(1)=-2 #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#there is a contradiction between (1) and (2)#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#How come? #ed_op#/DIV#ed_cl#