On 18/06/2010 4:27 AM, WM wrote: > On 17 Jun., 15:56, Sylvia Else<syl...@not.here.invalid> wrote: >> On 15/06/2010 2:13 PM, |-|ercules wrote: >> >> >> >> >> >>> Consider the list of increasing lengths of finite prefixes of pi >> >>> 3 >>> 31 >>> 314 >>> 3141 >>> .... >> >>> Everyone agrees that: >>> this list contains every digit of pi (1) >> >>> as pi is an infinite digit sequence, this means >> >>> this list contains every digit of an infinite digit sequence (2) >> >>> similarly, as computable digit sequences contain increasing lengths of >>> ALL possible finite prefixes >> >>> the list of computable reals contain every digit of ALL possible >>> infinite sequences (3) >> >> Obviously not - the diagonal argument shows that it doesn't. >> > > There is no diagonal element for a list of finite lines.
The list of computable reals is not a list of finite lines.
