In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 29 Mai, 05:51, William Hughes <wpihug...@hotmail.com> wrote: > > On May 27, 11:04 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > > > > But frequently I made use of what you call quatifier exchange and what > > > is allowed in case of complete linear sets. > > > > Nope. > > > > It is easy to show > > > > quantifier exchange is allowed for linear sets > > if and only if there is a largest element. > > > Rules of logic were obtained from finite sets. Rules of logic for > linear sets were obtained from linear finite sets.
But we have linear (meaning well ordered) non-finite sets outside of WM's wee wee word of MathUnrealism. > > Everything else is matheology of Wolkenkuckucksheim. > > Proof: A complete linear set without a last element is self > contradictory, as can be proven by the only logical rules that must be > accepted, namely those obtained from finite sets.
If only finite sets can exist then there are only finitely many of them , and the union of all finitely many of them must itself be a finite set: a finite universe outside of which there can be nothing to add to it when the things inside are used up.
But if there are only finitely many elements in that universal set, then WM's potentially infinite sets, being of necessity subsets of a finite universal set, can not be potentially infinite, as they must eventually exhaust their finite universal set.
So WM's own rules kill off his idiotic notion of potential infiniteness.