
Re: Another AC anomaly?
Posted:
Dec 13, 2009 10:31 PM


"K_h" <KHolmes@SX729.com> writes:
> It violates the spirit of what a limit is in some cases. So, > although it is sensible, it is not perfectly sensible.
Yeah, the discrete topology is different than other topologies.
But the standard topology on N is the discrete topology, too! Thus, the standard definition of sequence convergence on N is inherited via the subspace topology from Set. That is, a sequence {a_n  n in N} c N converges (in N) to m iff
(E k)(A j > k) a_j = m.
This is (unless I'm just buttwrong) the same as the definition of sequence convergence on Set restricted to the subspace N.
So it seems to me that you either dislike the discrete topology (which is certainly a bit odd) or you just dislike the discrete topology on Set. The latter opinion is a bit odd, too.
 "[Criticizing JSH's mathematics will result in] one of the worst debacles in the history of the world. It is foretold in most mythologies and religions. And yes, you are the ones, the cursed ones, who destroy the world." James S. Harris reads from the Aztec Book of the Damned Mathematicians

