[联谊] 0.999....=1 ?

xh_shadow · 发表于 2003-8-29 08:27

Just a ramdom post, i know probably no one cares, but,

0.333....+0.333....+0.333....=0.999....

0.333....=1/3

1/3 + 1/3 + 1/3 = 1

so 0.999.... = 1 ?

Who can explain this??? If you think this is dumb, just ignore me.

FIFA · 发表于 2003-8-29 12:58

since you have suppose the 2nd equation is correct, so you can draw your conclusion directly from that, which also means that the 1st and 3rd are unnecessary.

Well, here is more standard deduction:

set:
X = 0.9999.....  (1)
multiply 10 for equation (1):
10X = 9.9999.... (2)
equation (2) minus (1):
9X = 9          (3)
so,
X = 1          (4)

The conclusion can be drawn from equation (1) and (4): 0.9999..... = 1

xh_shadow · 发表于 2003-8-29 13:39

Thanks FIFA for providing this alternative method to prove the equation, 0.999....=1.
I did a research on GOOGLE.COM, and found some other methods to prove it. So 0.999....=1? weird, huh? Is it a well-known worldwide mathematical problem?

folle · 发表于 2003-8-29 13:59

1/3=0.3333333333...?
- 不成立，应为你写不出来这么多3,这个数字没有止境所以也就不存在一个数字等于另一个抽象的数字。
否则 1/0.9999999...=1.000...1
1.000...1的无穷次方=无穷大
=〉0.999999....=0?

苹果酸酸的 · 发表于 2003-9-1 18:45

因为你犯了个基本错误，那就是1/3不等于0.3333333
而是约等于.......
所以...............呵呵

canusa · 发表于 2003-9-1 19:38

这分明是在讨论高中的最简单的极限概念。本人刚高中毕业。

0.333....在数学上表示小数点后面有无限个3。

1.000...1的无穷次方=无穷大？笑话！

1.000...1表示小数点后面有无穷多个0。在数学上，这个关系可以表示成：

y=(1+1/x)^x

When x-->无穷大, y=1

steven_1214 · 发表于 2003-9-1 20:01

1 = 正整数
2 = 正整数

1 = 2 ？？？？？？？？？？？？？

工作日记 · 发表于 2003-9-1 20:29

0.9999...就是等于1呀。有什么奇怪的。

folle · 发表于 2003-9-2 08:56

to : canosa,
你的推断让我五体投地。

new_life · 发表于 2003-9-3 12:23

本来0.9999....就是等于1, 还要讨论半天。