The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
William Elliot

Posts: 2,637
Registered: 1/8/12
Posted: May 2, 2013 10:59 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Tue, 30 Apr 2013, Butch Malahide wrote:
> On Apr 29, 11:28 pm, Butch Malahide <> wrote:
> > On Apr 29, 9:17 pm, William Elliot <> 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)?

> > I'll bet that that bijection is a homeomorphism. It would be really
> > amazing if it weren't, wouldn't it?


Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.