On 18 Jun., 03:42, "|-|ercules" <radgray...@yahoo.com> wrote: > "Transfer Principle" <lwal...@lausd.net> wrote > > > > > > > On Jun 17, 6:56 am, Sylvia Else <syl...@not.here.invalid> wrote: > >> On 15/06/2010 2:13 PM, |-|ercules wrote: > >> > the list of computable reals contain every digit of ALL possible > >> > infinite sequences (3) > >> Obviously not - the diagonal argument shows that it doesn't. > > > But Herc doesn't accept the diagonal argument. Just because > > Else accepts the diagonal argument, it doesn't mean that > > Herc is required to accept it. > > > Sure, Cantor's Theorem is a theorem of ZFC. But Herc said > > nothing about working in ZFC. To Herc, ZFC is a "religion" > > in which he doesn't believe. > > > Else's post, therefore, is typical of the posts which seek > > to use ZFC to prove Herc wrong. > > To say the list of computable reals DOES NOT contain every digit (in order) of ALL possible > infinite sequences > > is to say this list does not contain every digit (in order) of PI. > > 3 > 31 > 314 > ...
Pi is constructable and computable and definable, because there is a finite rule (in fact there are many) to find each digit desired. But as there are only countably many finite rules, there cannot be more defined numbers. Therefore matheologicians have created undefinable "numbers". It is impossoible to know anything of such a "number". Therefore they are not numnbers and, moreover, they cannot be generated as anti-diagonal numbers in Cantor lists. Hence, the "monnshine numnbers" in fact do not help to save set theory. They are nothing but nonsense but addicts of set theory selectively exclude every impression that could wake them up. It is impossible to convert lost set theorists, but it may be possible to save some souls.
