Re: Well Ordering the Reals

Tony Orlow says...

>If one can, as you did, select an infinite element, can form a set by
>considering elements finitely less than that element, then any "uncountable"
>set has subsets which are "infinite" descending chains.

So you are saying that no uncountable set can be well-ordered.
So you *don't* claim to have a well-ordering for the reals?

--
Daryl McCullough
Ithaca, NY

.

Relevant Pages

  • Re: Well Ordering the Reals
    ... Daryl McCullough said: ... > Tony Orlow says... ... >>If one can, as you did, select an infinite element, can form a set by ... > So you are saying that no uncountable set can be well-ordered. ...
    (sci.math)
  • Re: infinity
    ... Tony Orlow wrote: ... then it contains an infinite element. ... No, you can't _show_ us anything, mathematically speaking, because you ... consider a binary tree in which there are only branching nodes - how ...
    (sci.math)
  • Re: An uncountable countable set
    ... Tony Orlow wrote: ... defines an infinite element of *N as being "larger than any finite ... But none of Robinson's non-standard numbers are cardinalities. ... No kidding. ...
    (sci.math)
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