In article <email@example.com>, firstname.lastname@example.org wrote:
> On Wednesday, 30 April 2014 23:54:10 UTC+2, Virgil wrote:
> > > > > I am convinced Zermelo did not know or at least did > > > > > not use this distinction. Of course he wanted to express that set > > > > > theory > > > > > is apparently fruitful
> > > But I declared this as my opinion.
> > So your opinion is that Zermelo regarded set theory as fruitful!
> He could no prove it, but of course he believed it.
> > And most of us rate Zermelo's opinion as worth far more than WM's,
> Those need to accept undefinable "real" numbers, i.e., numbers that cannot be > mentioned in any way by men.
Then WM must not be a man at all , since he just mentioned them.
They are not individually defineable, i.e., cannot be given an exact value, in the same way that naturals, integers, and rationals can be given exact values, but every real interval of positive length contains uncountably many of them.
It is quite possible to mention them, even WM can do that, it is just impossible to specify a precise value for any one of them.
> Of course there are such Fools Of Matheology, as > I call them, but most mathematicians would not join them.
Those whom WM insults as being "Fools Of Matheology" incude those at the forefront of modern mathematics
MOST mathematicians already HAVE joined with them, at least to the extent of having infinitely many natural numbers, rational numbers , real numbers, etc., so do not need to join again. > > > so if WM is right, then WM is also wrong! > > But not vice versa?