送交者: HunHunSheng 于 2005-11-01, 14:14:15:

回答: 怎么知道一个数十无限不循环小数？怎么知道PI是无限不循环小数？ 由 coubert 于 2005-11-01, 14:07:55:

if sqrt(2) is a 无限循环小数, then it
can be expressed as n/m where n and m has no common divisior.

so 2=n^2/m^2.

so n must be an even number can can be expressed as 2k.

so 2=4k^2/m^2

so m^2=2k^2.

so m must be an even number too.

so n and m has a common dividor =2, this contradict
previous assumption.

So sqrt(2) can not be a 无限循环小数,

• 昏昏混事儿呢？证明派是无限不循环。 - 无知 (0 bytes) 2005-11-01, 16:42:50
  • 一张CD背后就可以写下的证明：派无限不循环 - NE0 (256 bytes) 2005-11-03, 10:41:34
    • 图在这里。 - NE0 (82 bytes) 2005-11-03, 10:44:48
• thanks - coubert (0 bytes) 2005-11-01, 14:15:17

加跟贴