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Re: Matheology 400: WM's Quantifier Confusion
Posted:
Dec 11, 2013 5:58 AM


Virgil <virgil@ligriv.com> writes:
> In article <9b81b6f99f554559917995ead66d0b88@googlegroups.com>, > WM <wolfgang.mueckenheim@hsaugsburg.de> wrote: > >> Am Dienstag, 10. Dezember 2013 14:01:30 UTC+1 schrieb wpih...@gmail.com: >> > >> > Then you know that for a constructivist there is no list of >> > all real numbers. > > For a constuctivist there is also no complete list of all rational > numbers.
??
There's no problem in giving an effective function from N to the rationals. The intuitionist position is that the rationals are therefore countable. (WM's claim to the contrary notwithstanding.)
There *is* a problem giving such a function from N to the computable reals.
>> Here we need a list of all rational numbers only. > > Which, other than for constructivists is easy enough. > >> This list can be diagonalized. The first few digits of the >> antidiagonal cannot prove that the antidiagonal differs from all >> rational numbers of the list. > > But a general rule, applied equally to all digit positions, can.
Exactly.
 Alan Smaill



