Re: infinity


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

.

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