On 31 Jan., 01:51, "Jesse F. Hughes" <je...@phiwumbda.org> wrote: > david petry <david_lawrence_pe...@yahoo.com> writes: > > On Wednesday, January 30, 2013 1:58:25 PM UTC-8, Toni...@yahoo.com wrote: > > >> How in the world can a serious MATHEMATICIAN _claim_ that something written in a book/paper has proved "once and for all" that so and so and then, later, he whines he has no expertise, interest and etc. in the paper/book's claims TO DO SO?? > > > The word "proof" has two meanings: > > > 1) Informally, a proof is a compelling argument using the > > intuitively understood reasoning that we have acquired from our > > experience in the real world. It is entirely possible that that > > intuitively understood reasoning has never been completely and > > accurately formalized. > > > 2) A purely formal construct that is inspired by the informal notion > > of proof but may not be an entirely accurate model of that informal > > notion. > > > When we debate the question of whether ZFC has accurately captured > > our intuitive notion of what a proof is, we must rely on the first > > definition. It is reasonable for mathematicians to get involved in > > such a debate. > > WM has bigger fish to fry. > > He thinks that he's proved ZF is inconsistent,
Why depend on my arguments? ZFC, at least, has been proven inconsistent, if 2 is not 1. Remember Hausdorff-Banach-Tarski. There we start from the statement V = 1 and find after applying some equivalence relations V = 2.
Thereby it is completely irrelevant whether "unmeasurable point sets" are involved or not. What counts is simply the first and the second statement. Therefore ZFC has been proven inconsistent already - at least for every sober non-matheologian.
> > I don't know if that's what he's doing on p. 112, mind you, but at > least sometimes, he is presenting what he mistakenly believes is a > valid, mathematical proof.
I apply the rule that in mathematics identical exercises have to yield identical results.
In analysis the continued fraction ((((((10^0)/10)+10^1)/10)+10^2)/10)+...
has the (improper) limit oo. In ZFC the sequence yields the limit < 1.
Everybody who is not wearing blinkers can recognize here that ZFC is not compatible with mathematics. Small wonder that a sober mathematician accepts that argument until he is reminded, after a while, by some colleagues that they are of different opinion and he is not a recognized expert of matheology.