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Re: Matheology § 258
Posted:
May 1, 2013 4:07 PM


Virgil <virgil@ligriv.com> writes:
> In article > <09c1007379cd4fbcb391765f13db7a9c@k8g2000vbz.googlegroups.com>, > WM <mueckenh@rz.fhaugsburg.de> wrote: > >> On 1 Mai, 11:15, Dan <dan.ms.ch...@gmail.com> wrote: >> > > It is necessary for Cantor's proof. Unless every digit exists on the >> > > diagonal, the diagonal number is undefined in an undefined list. But >> > > that is Cantor's claim: forall n : a_nn =/= d_n. >> > >> > It exists "as formula" , whether or not you know the formula . >> >> There are only countably many formulas. If all diagonals exist as >> formulas, then all belong to a countable set. > > But if there were only countably many reals, one only needs countably > many formulas to find the nth digit of the nth real.
In fact WM tells us that there is a single finite description P(n,m) of the paths through the binary tree such that for every pair of naturals n,m, P(n,m) characterises the nth digit of the mth path.
 Alan Smaill



