Re: Cantor Confusion

In article <45757FEB.5030804@xxxxxxxxxxxxxxxxxxx>,
Eckard Blumschein <blumschein@xxxxxxxxxxxxxxxxxxx> wrote:

On 12/5/2006 12:39 AM, Virgil wrote:

If irrational numbers are thought
to complete the rationals which sounds quite logical, then the
constituted entity of the reals has to be as fictitious as the
irrationals.

And the rationals and the naturals and all other mathematical
constructions.

No. No. No.

Yes! Yes! Yes!

I do not have a more apt word than fictitious in the sense
it was used by Leibniz in order to stress the conceptual difference
between addressable discrete numbers and merely attributed without such
address positions. If you deny this conceptual difference, then you are
denying the difference between generally countable rationals on one
sinde and generally uncountable just fictitious reals on the other side.

There is already a word, "irrational" that conveys everything that is
needed. "Fictitious" applies equally well to every number.

In other words: Genuine numbers are countable, fictitious numbers are
uncountable. The latter do not have an available numerical address.


They are all equally fictitious, creations of the mind having no
existence outside of the mind.

This is an attempt to hide that Dedekind and Cantor built an Utopia.

The labels "genuine" and "fictitious" are equally an attempt to hide the
reality that your supposedly "genuine" numbers are no more genuine than
any others, nor your supposedly "fictitious" numbers are no more
fictitious, than any others, in the everyday meaning of those labels.
.

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