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Topic: Another AC anomaly?
Replies: 43   Last Post: Dec 21, 2009 8:08 AM

 Messages: [ Previous | Next ]
 Jesse F. Hughes Posts: 9,776 Registered: 12/6/04
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 butt-wrong) 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

Date Subject Author
12/12/09 Jesse F. Hughes
12/13/09 K_h
12/14/09 Dik T. Winter
12/14/09 K_h
12/15/09 Dik T. Winter
12/15/09 K_h
12/16/09 Dik T. Winter
12/16/09 K_h
12/17/09 Dik T. Winter
12/18/09 K_h
12/18/09 Dik T. Winter
12/18/09 K_h
12/21/09 Dik T. Winter
12/14/09 Dik T. Winter
12/14/09 K_h
12/15/09 Dik T. Winter
12/15/09 Dik T. Winter
12/15/09 K_h
12/16/09 Dik T. Winter
12/17/09 K_h
12/17/09 Dik T. Winter
12/18/09 K_h
12/18/09 K_h
12/18/09 Dik T. Winter
12/18/09 K_h
12/18/09 Dik T. Winter
12/18/09 K_h
12/15/09 K_h
12/16/09 Jesse F. Hughes
12/17/09 Dik T. Winter
12/17/09 Jesse F. Hughes
12/16/09 Dik T. Winter
12/15/09 ross.finlayson@gmail.com
12/13/09 K_h
12/13/09 Jesse F. Hughes
12/13/09 Jesse F. Hughes
12/14/09 Ilmari Karonen
12/14/09 Jesse F. Hughes
12/15/09 Chas Brown