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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 10:52 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 butt-wrong) the same as the definition of
> sequence convergence on Set restricted to the subspace N.

Yeah, well, I am just butt-wrong, 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

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