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Topic: N^N
Replies: 10   Last Post: May 12, 2013 9:34 AM

 Messages: [ Previous | Next ]
 Butch Malahide Posts: 894 Registered: 6/29/05
Re: N^N
Posted: May 3, 2013 12:53 AM

On May 2, 9:59 pm, William Elliot <ma...@panix.com> wrote:
> On Tue, 30 Apr 2013, Butch Malahide wrote:
> > On Apr 29, 11:28 pm, Butch Malahide <fred.gal...@gmail.com> wrote:
> > > On Apr 29, 9:17 pm, William Elliot <ma...@panix.com> wrote:
>
> > > > Why in N^N homeomorphic to R\Q?
>
> > > R\Q is homeomorphic to the space of *positive* irrational numbers. The
> > > simple continued fraction expansion is a natural bijection between the
> > > positive irrationals and the space N^N.

>
> > Where by "positive irrationals" I mean irrationals between 0 and 1.
>
> How so?  The continued fraction for positive integers a1, a2,..
> [a1, a2,.. ] = a1 + 1/(a2 + 1/(a3 + ..))
>
> Would not those continued fractions not be
> limited to (0,1) but to (0,oo)?

By (0,oo) do you mean (1,oo)?

Date Subject Author
4/29/13 William Elliot
4/29/13 Tanu R.
4/30/13 Butch Malahide
4/30/13 Butch Malahide
5/2/13 William Elliot
5/3/13 Butch Malahide
5/3/13 William Elliot
5/3/13 Butch Malahide
5/10/13 Leon Aigret
5/11/13 William Elliot
5/12/13 Leon Aigret