Re: *** T. Winter says: Definition: sum{i in N} i = 0

In article <1183010585.533065.309210@xxxxxxxxxxxxxxxxxxxxxxxxxxxx> WM <mueckenh@xxxxxxxxxxxxxxxxx> writes:
On 28 Jun., 02:28, "*** T. Winter" <***.Win...@xxxxxx> wrote:
....
> I said: Cantor "proved" well-ordering of a set step by step, even for
> uncountable sets.
> You said: I do not think he proved anything of that kind.
> The set of all cardinals is uncountable. So you are wrong.

What other uncountable sets did he prove it for?

The set of all Cardinals - {1}, the set of all cardinals - {1,
2}, ..., the set of al cardinals of second number class, ..

But not for the set of reals.

> > He *assumed* well-ordering was possible for all sets, but
> > did not prove that.
>
> No, he thought to have proved it, but was wrong.

Yes, so he did not prove it, and so assumed it.

He proved that (in his opinion) just as you may "prove" in your
opinion that the continumm is uncountable.

Well, where is the prove (by Cantor) that the reals can be well-ordered?

> No again. Hausdorff continued that this method is not a proof but is
> wrong, because it implies a construction. This quote only shows that
> early set theorists used to make his error.

Early set theorists made many errors. So why the emphasis on the error
of Hausdorff?

His remarks demonstrate that you are wrong.

Makes no sense.

> That has nothing to do with Zenon. Zenon "forgot" that you need only
> half the time for half the way (at constant velocity).

Yes, so what? If space is quantified you cannot halve the distance any
more in a non-continuous model. And I wonder what happens if time is
quantified.

All that has not the least to do with Zenon, because he failed to
consider time at all. That was the reason of is paadoes.

And as time is not a mathematical concept, his paradox is not a mathematical
paradox.
--
*** t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~***/
.

Quantcast