(phi( <[1] 2 3 4...> ) & An (phi ( <[1 2 ... n] n+1 n+2 ...>) -> phi( <[1 2 ... n n+1] n+2 n+3 ...> ))) -> phi( <[1 2 3 4...]> )
in [Math]
|
Prev: How Can ZFC/PA do much of Math - it Can't Even Prove PA isConsistent (EASY PROOF)
Next: Modularity of Mind
From: |-|ercules on 30 Jun 2010 20:59 Behold the Cantor killer! phi( <[1] 2 3 4...> ) & An (phi ( <[1 2 ... n] n+1 n+2 ...>) -> phi( <[1 2 ... n n+1] n+2 n+3 ...> )) -> phi( <[1 2 3 4...]> ) Prefix Induction Schema If a property holds for the 1st element in a sequence, and if it holds for the first n elements in a sequence then it holds for the first n+1 elements in a sequence, then the property holds for all elements in the sequence. It can be used to prove all possible sequences of digits are listable, namely this limit exists (the sequences are infinite). As the length of the list of computable reals->oo, the length of all possible digit sequences on the list->oo. Herc
From: Dingo on 30 Jun 2010 21:17
On Thu, 1 Jul 2010 10:59:28 +1000, "|-|ercules" <radgray123(a)yahoo.com> wrote: This has no relevance whatsoever to aus.tv - stop posting to it, and others please delete aus.tv when replying to it. >Behold the Cantor killer! > >phi( <[1] 2 3 4...> ) & An (phi ( <[1 2 ... n] n+1 n+2 ...>) -> phi( <[1 2 ... n n+1] n+2 n+3 ...> )) >-> >phi( <[1 2 3 4...]> ) > > >Prefix Induction Schema > >If a property holds for the 1st element in a sequence, and if it holds for the first n elements in a sequence >then it holds for the first n+1 elements in a sequence, then the property holds for all elements in the sequence. > >It can be used to prove all possible sequences of digits are listable, namely this limit exists (the sequences are infinite). > >As the length of the list of computable reals->oo, the length of all possible digit sequences on the list->oo. > >Herc |