Re: Well Ordering the Reals

Daryl McCullough said:
> Tony Orlow says...
>
> >Oh come on. That set has one element, not an infinite number. Do you know what
> >"number of" means?
>
> Nobody knows what *you* mean by "number of elements". They know
> what people *normally* mean, but you have explicitly rejected that
> definition.
You HAVE no definition for number of elements for infinite sets. You have
cardinality instead, which is not a particular number of elements, but an
equivalence class that ignores actual numbers. I don't reject bijections. I
just consider them insufficient in themselves to declare equal set size or
number of elements. It's a different animal.
>
> --
> Daryl McCullough
> Ithaca, NY
>
>

--
Smiles,

Tony
http://www.people.cornell.edu/pages/aeo6/WellOrder/
.

Relevant Pages

  • Re: Well Ordering the Reals
    ... >> Tony Orlow says... ... >> Daryl McCullough ... > variable which can assume infinite values. ... nug tnahpele knip a htiw ti toohs dna knip seog ti litnu eson sti ...
    (sci.math)
  • Re: infinity
    ... >> Tony Orlow says... ... finite or infinite. ... Daryl McCullough ... Prev by Date: ...
    (sci.math)
  • Re: infinity
    ... Daryl McCullough said: ... > Tony Orlow says... ... the set is unbounded but not infinite. ... > What is the size of the set of all finite naturals? ...
    (sci.math)
  • Re: infinity
    ... > Tony Orlow wrote: ... >>Daryl McCullough said: ... > For all s a finite string, ... all lengths are finite, then none are infinite, and the language cannot be ...
    (sci.math)
  • Re: Well Ordering the Reals
    ... >> Daryl McCullough said: ... >>> Tony Orlow says... ... >> I already defined finite, infinite and infinitesimal quantities, ... It has as much to do with set sizes as your injections do with quantities. ...
    (sci.math)
Loading