Re: Orlow cardinality question

stephen@xxxxxxxxxx said:
> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
> > Virgil said:
> >>
> >> Axioms are unfounded. That is the nature of axioms.
> > Not good ones. Axioms should be well-considered, and not generated willy-nilly.
>
> So which of the axioms of set theory do you object to. Here is a list.
>
> http://mathworld.wolfram.com/Zermelo-FraenkelAxioms.html
>
> >>
> >> There may be reasons for choosing a particular set of axioms, but, once
> >> chosen, they are all that one is allowed to consider in deciding what
> >> follows from them.
> > Allowed? Tie your own hands, not mine. In my world, any axiom which is assumed
> > true may be used in any argument.
>
> So when someone is discussing Spherical Geometry, you think it
> is perfectly valid to make arguments using Euclids Fifth Postulate?
>
> Stephen
>
Euclid's fifth is only true in the context of euclidean space. There are more
general rules which can be applied. Certainly you are not sugesting that S^L as
a measure of a set of generated strings is inappropriate for some reason in the
context of sets? Does set membership allow one to make unique strings that have
the same series of symbols? No. The rule still applies.
--
Smiles,

Tony
.

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