In article <firstname.lastname@example.org>, email@example.com wrote:
> On Saturday, 15 June 2013 22:22:30 UTC+2, Virgil wrote: > > > I *never* leave the domain of finite sets (like Cantor never leaves it > > > when enumerating something with finite naturals). > > > Then WM's set of rationals must be a finite set, in contrast to everyone > > else's sets of rational > > No. I never leave the finite domain, but I never come to an end.
Does WM still claim that any union of finite sets is finite?
If so then WM's rules do not govern anywhere that that claim is false.
And as WM cannot PROVE that all set are finite without first assuming it, none of his proofs dependent on that assumption are valid when his assumption cannot be shown to be necessary.
Which assumption, WM has failed to show necessary to the satisfaction of anyone other than WM himself.
As for well-ordering the rationals in standard order, any finite ordered set is automatically well-ordered, but infinite ordered sets need not be, so whenever infinite sets are allowed, like for the standard set of rationals, one can have infinite ordered sets which are not well-ordered.
In fact, for ANY well-ordered infinite set, that set with the reverse ordering is NOT well-ordered.
And WM's claim that everyone must limit themselves to only finite sets is a delusion that cripples him and leaves him unable to do any serious mathematics. --