证明0.999…=1

数学中最妙不可言的部分是其简洁优美的陈述,它们常常会让人惊呼“这不是真的”,例如e^(iπ)+1=0。在《蒙大拿州数学爱好者》杂志上,两位研究人员用了28页探讨了一个已经被深入讨论过的、但常常让学生感到困惑的问题:0.999…等于1(PDF)。 众所周知,循环小数0.999…等于实数1,相关的证明很多,例如:设a= 0.999…,两边同乘以10得到10a=9.99…,等式两边再减去a得到10a-a=9,即9a=9,a=1;另一个证明,1/9 = 0.111…,9 x (1/9) = 0.999…于是1 = 0.999…。

Advertisements
Post a comment or leave a trackback: Trackback URL.

发表评论

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / 更改 )

Twitter picture

You are commenting using your Twitter account. Log Out / 更改 )

Facebook photo

You are commenting using your Facebook account. Log Out / 更改 )

Google+ photo

You are commenting using your Google+ account. Log Out / 更改 )

Connecting to %s

%d 博主赞过: