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Re: My set theory
Posted:
Apr 7, 2014 7:32 AM


Virgil <virgil@ligriv.com> writes:
> In article <87wqf5oryn.fsf@uta.fi>, > Aatu Koskensilta <aatu.koskensilta@uta.fi> wrote: > >> Peter Percival <peterxpercival@hotmail.com> writes: >> >> > I think that in a theory of sets without the axiom of choice there can >> > be noncomparable cardinalities. >> >> Sure. But even in such theories the inequality N < R will hold, >> witnessed by the injection taking the natural n to the real n. > > That would certainly justify N <= R, but why would it necessitate > strict inequality?
By the uncountability of the reals. In any case, this more or less trivial injection  the identity map, morally speaking  suffices to establish comparability.
 Aatu Koskensilta (aatu.koskensilta@uta.fi)
"Wovon man nicht sprechen kann, darüber muss man schweigen"  Ludwig Wittgenstein, Tractatus LogicoPhilosophicus



