Re: Review of Mueckenheims book.

In article <1172770795.066009.29180@xxxxxxxxxxxxxxxxxxxxxxxxxxx> mueckenh@xxxxxxxxxxxxxxxxx writes:
On 1 Mrz., 03:30, "*** T. Winter" <***.Win...@xxxxxx> wrote:
> You cannot express the base sqrt(2) by the unit 1.

But the expression I use is precise enough to do calculations with it.

Yes, it is a fairly good approximation.

In what way is it an approximation? You think that the factorisations that
have been calculated by the Number Field Sieve are only approximations?

You are leaving the realm of reality.

I entered it.

Your view of reality.

If a definable well-ordering is shown to exist (without other axioms
than ZFC),

But you leave out the model.

then the following statement of Fraenkel et al. is wrong:
Let us chose s to be the set of all well-orderings of the real
numbers; ... one cannot prove in ZFC that s contains any definable
member as one cannot prove in ZFC that there is a definable well-
ordering of the set of all real numbers.

Yes, you can not prove it in ZFC. But even when you define the real
numbers from ZFC, you need axioms to get them. And with those
additional axioms you may, or may not, get a definable well-ordering.

But apparently you fail to see the distinction.

I fail to see many things you believe to see. But here you clearly
prove that these things really aren't there.

Yes, you fail to see a lot of things.
--
*** t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~***/
.