設x=0.999...,則10x=9.999...
所以10x-x=9.999...-0.999...
卽9x=9,故x=1,也就是0.999...=1
完畢
cws 寫到:凱凱 寫到:#ed_op#DIV#ed_cl#我覺得#ed_op#U#ed_cl#1/3=0.33333333....#ed_op#/U#ed_cl#這是在#ed_op#STRONG#ed_cl#除不盡#ed_op#/STRONG#ed_cl#的狀況下#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#U#ed_cl#0.999999999999......./3=0.33333333......#ed_op#/U#ed_cl#這是在#ed_op#STRONG#ed_cl#除的盡#ed_op#/STRONG#ed_cl#的情況下#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# 不能以看答案的方式就說#ed_op#U#ed_cl#1#ed_op#/U#ed_cl#和#ed_op#U#ed_cl#0.9999999....#ed_op#/U#ed_cl##ed_op#STRONG#ed_cl#相等#ed_op#/STRONG#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#就如#ed_op#STRONG#ed_cl#翼虎大大#ed_op#/STRONG#ed_cl#所說的,#ed_op#U#ed_cl#0.999...#ed_op#/U#ed_cl#是#ed_op#STRONG#ed_cl#趨近#ed_op#/STRONG#ed_cl#於#ed_op#U#ed_cl#1#ed_op#/U#ed_cl#,#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# 它們的#ed_op#STRONG#ed_cl#差距#ed_op#/STRONG#ed_cl#是#ed_op#U#ed_cl#0.000......0001#ed_op#/U#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#~~~~~~~~~~~~~by 凱凱#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl#
如果1-0.999..... =0.000.....1
所以0.999.....+0.000.....1=1,0.999.....是有限個小數位
但因為0.999.....是一個無盡的小數
故0.999.....+0.000.....1=1.000......999......
因為0.000.....1不是無窮小數
雖然0.999.....是趨近1
但當0.999.....是一個有無限個小數位的數,就不會有那個0.000.....1
所以我認為0.999....=1
凱凱 寫到:#ed_op#DIV#ed_cl#我覺得#ed_op#U#ed_cl#1/3=0.33333333....#ed_op#/U#ed_cl#這是在#ed_op#STRONG#ed_cl#除不盡#ed_op#/STRONG#ed_cl#的狀況下#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#U#ed_cl#0.999999999999......./3=0.33333333......#ed_op#/U#ed_cl#這是在#ed_op#STRONG#ed_cl#除的盡#ed_op#/STRONG#ed_cl#的情況下#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# 不能以看答案的方式就說#ed_op#U#ed_cl#1#ed_op#/U#ed_cl#和#ed_op#U#ed_cl#0.9999999....#ed_op#/U#ed_cl##ed_op#STRONG#ed_cl#相等#ed_op#/STRONG#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#就如#ed_op#STRONG#ed_cl#翼虎大大#ed_op#/STRONG#ed_cl#所說的,#ed_op#U#ed_cl#0.999...#ed_op#/U#ed_cl#是#ed_op#STRONG#ed_cl#趨近#ed_op#/STRONG#ed_cl#於#ed_op#U#ed_cl#1#ed_op#/U#ed_cl#,#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# 它們的#ed_op#STRONG#ed_cl#差距#ed_op#/STRONG#ed_cl#是#ed_op#U#ed_cl#0.000......0001#ed_op#/U#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#~~~~~~~~~~~~~by 凱凱#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl#
鐵傲翼虎 寫到:若以積分的方法去算就可以得知此結果
不過應該不能說"等於"
而是"趨近於"
在計算上為了方便(誤差直極小可省略)可以省略不計
這樣解釋可以嗎??
~~~~~~~~~翼虎