Re: Well Ordering the Reals

Randy Poe wrote:
> Tony Orlow wrote:
> > Randy Poe said:
> > > So I'm not sure what the general expression is for elements of the
> > > minimal set obeying these rules, though it's clear that any
> > > such element must be obtained by a finite number of operations
> > > beginning with 0, and that clearly rules out uncountably many
> > > real numbers.
> > >
> > > What was this set intended to be?
> > This is the set of all real numbers,
>
> No it's not. It's the set of numbers which can be generated by
> finite application of 2^x or -2^x.
>
> > defined inductively. It's a simplified,
> > infinity-free version of the well-ordering presented on my page. Certainly, no
> > countable
>
> The set as defined is composed of FINITELY-generated values.

Aw, come on, you're running scared, aren't you, Randy Poe? Why stop at
the portals of the Twilight Zone? You've already got within an
infinitieth of a smidgen (or thereabouts) of every real, so just let
your boat be guided into the tunnel. You'll soon get to enjoy the
indefinite sensation, and in what seems only like, er, well, about the
last 1/3 of eternity, I should say, you'll sail out into the brightly
sunlit Pool of Infinity, surrounded by mermaids of such intense beauty
that you completely forget what the original question was. I have, too,
rather. Have you ever seen the Monty Python crew's film "Erik the
Viking"? It's very good.

> > number of iterations will generate all real numbers exactly,

Ah, yeah. Well, whatever.

Brian Chandler
http://imaginatorium.org

.

Relevant Pages

  • Re: infinity
    ... > Tony Orlow wrote: ... >> Randy Poe said: ... I'm not talking for the moment about this notation. ... member of the set of naturals starting at 0. ...
    (sci.math)
  • Re: Well Ordering the Reals
    ... >> Tony Orlow wrote: ... > Aw, come on, you're running scared, aren't you, Randy Poe? ... The mermaids ARE very beautiful, but not always very merciful, so be careful ... > Brian Chandler ...
    (sci.math)
  • Re: infinity
    ... > Tony Orlow wrote: ... >> Randy Poe said: ... The members of the one set are the inverses of the members of the ... > the infinite expanse". ...
    (sci.math)
  • Re: infinity
    ... > Tony Orlow wrote: ... >> Randy Poe said: ... In the finites, all differences are less than oo. ... > little redundant. ...
    (sci.math)
  • Re: infinity
    ... > Tony Orlow wrote: ... >> Randy Poe said: ... Proof by faith. ... > infinite elements. ...
    (sci.math)