
Re: Another AC anomaly?
Posted:
Dec 13, 2009 10:52 PM


"Jesse F. Hughes" <jesse@phiwumbda.org> writes:
> "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.
Yeah, well, I am just buttwrong, ain't I?
I was confusing the discrete space of Set with what the Wikipedia article calls "general set convergence".
My mistake.
 Jesse F. Hughes
"You know that view most people have of mathematicians as brilliant people? What if they're not?"  James S. Harris

