On 31 Jan., 10:49, Virgil <vir...@ligriv.com> wrote: > In article > <2c0c03e1-d70b-484c-997b-76bd1397d...@h2g2000yqa.googlegroups.com>, > > WM <mueck...@rz.fh-augsburg.de> wrote: > > 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: > > > > 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. > > I am not aware that the Banach-Tarski model of geometry has ever > successfully been imbedded in ZFC. > > And until WM can establishes that the Banack-Tarski theorem can be > stated and proven in ZFC, it poses no problem to ZFC, and even then > would pose no problem in ZF. > > > > > 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. > > Meaning only in Wolkenmuekenheim. > > > > > > 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)+... > > That does not appear to be in the form of a continued fraction at all.
Is that your only escape? Call it however you like. Every initial segment is a fraction - and this is continued without end.
Imagine I put it as a homework. What is the limit? Do I have to accept oo as well as <1 or even something in between, depending on what mathematical tools are applied? By this trick every answer to every homework has to be accepted. Well, I know, it has been so for nearly one hundred years already. If the answer to 3 + 5 was 9, then the pupil could refer to Banach-Tarski: "Didn' t you mean marbles? Look, I have applied Banach-Tarski to one of them and so have doubled it." You think, I should grade that very good?