Re: infinity

Randy Poe said:
>
> aeo6 Tony Orlow wrote:
> > Randy Poe said:
> > > Ability to form a bijection is the definition of equal
> > > cardinality. As it is the definition, it is suitable to
> > > use it as a "sole criterion" for equal cardinality.
> > >
> > >
> > Fine, but then cantorians should have no objection to statements such as "the
> > set of naturals is twice as big as the set of evens", or, "there are twice as
> > many reals in [0,2) than in [0,1)". If cardinality doesn't claim to be the same
> > as the size of the set, then why are such statements rejected so strongly?
>
> Because there's no consistency in this notion of size, it
> leads easily into self contradiction.
>
> We like consistency.
>
> - Randy
>
>
Uh, yeah, right, like the same problem having multiple answers. What
consistency! What was the contradiction in the notion that [0,1) is half the
size of [0,2) again?
--
Smiles,

Tony
.

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