On 22/06/2010 10:44 AM, Sylvia Else 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) > > The discussion on permutations of lists of computable reals to construct > diagonals showed that it is possible to construct diagonals that have > any finite prefix. However, you were quick to point out that as the > computable reals contain numbers like 0.111111...., diagonals not > containing a 1 are impossible. > > That is to say, there is a set of reals which contains all possible > finite prefixes, but which does not contain all possible infinite > sequences. > > Since that contradicts the reasoning used to conclude your proposition > (3), you'd have to prove it some other way. > > Sylvia.
Looks like this is going to be ignored because it's inconvenient.