In article <firstname.lastname@example.org>, email@example.com wrote:
> On Friday, 2 May 2014 16:54:15 UTC+2, Dan Christensen wrote:
> > After over a century of intensive scrutiny,
> Wrong. Most mathematicians have simply accepted what their leaders said. Some > have really found contradictions but they have been silenced, i.e., their > papers have rarely been mentioned by the leading matheologians.
> > no one has been able to demonstrate any inconsistency arising from that the > > Peano's Axioms for the infinite set of natural numbers.
> There is no inconsistency if |N is interpreted as a potentially infinite set.
Having only potentially infinite but not actually infinite sets violates the LöwenheimSkolem theorem, which says, in part: The proof of the upward part of the theorem shows that a theory with arbitrarily large finite models must have an infinite model;
> But we know that every expression that can appear in eternity in the whole, > possibly infinite, universe belongs to a countable set.
But the setof all subsets, or power set, is of provably greater cardinality then the set itself, so the existence of even one countably infinite set requires the existene of uncountably infinite sets.
> Therefore also every > expression that can appear in the mathematical discourse belongs to a > countable set.
That may be true in WMytheological discourse, but not in mathematical ones, since as soon a as one has any countaby infnite set, one also has its finitely defined but uncountably infinite power set. > > Nothing that can appear in this discourse, which *is* mathematics, can be > uncountable.
So that WM requires existence of sets for which there are no sets of all subsets? > > We do *n* need any definition of "definition".
And WM certainly does not seem to have them all, if he rejects the definition of the power set of given set as being the set of all the origianal set's subsets.
> Not necessary to understand what I said above.
And proper mathematicians should avoid even trying, as it make no sense anywhere outside of WM's wild weird world of WMytheology. --