Re: how to list all of the real numbers

On Aug 24, 12:15 am, Jonathan Hoyle <jonho...@xxxxxxx> wrote:
On Aug 23, 7:04 pm, "Ross A. Finlayson" <r...@xxxxxxxxxxxxxxx> wrote:

It was nearly two years ago, and yes it was in that discussion
where your outline was proven to be faulty. I could go over
your logic flaw again, but it was detailed pretty well at the
time, and you might just simply re-read that posted topic to
refresh your memory.

Yes I should re-read it.

I think you would do well to. Despite the fact that it shows your
proof to be in error, I think it was an example of your best work
mathematically and logically. With a little effort, your
construction could be used as a proof for the existence of limit
ordinals.

I think what you mean here is: Given the existence of infinite
ordinals, it could be a proof that not all of them will be successor
ordinals (thus limit ordinals). One cannot simply "prove" the
existence of any ordinals without accepting certain relevant axioms.
Ross's errant modification of Cantor's Nested Interval Theorem cannot,
in and of itself, substitute for such axioms.

As an aside, I am not sure Ross even believes in limit ordinals
(despite his ironic "proof" of them). It is in these internal
contradictions which causes him to spew the tangled garbage he does.

.

Relevant Pages

  • Re: Galileos Paradox
    ... The existence of the set of natural numbers is used all over the place ... You are just FLAT OUT INCORRECT that non-standard analysis is ... DOES prove the existence of ordinals. ... Do the infinite forms of them jut off in other directions? ...
    (sci.math)
  • Re: Question regarding limit ordinals and transfinite cardinals.
    ... It does not prove the existence of any other limit ... cardinality than N. You need to prove that ordinals are totally ordered. ... The existence of limit ordinals except ... w is hardly a direct corollary of the axiom of infinity, ...
    (sci.logic)
  • Re: Question regarding limit ordinals and transfinite cardinals.
    ... It does not prove the existence of any other limit ... cardinality than N. You need to prove that ordinals are totally ordered. ... The existence of limit ordinals except ... w is hardly a direct corollary of the axiom of infinity, ...
    (sci.logic)
  • Re: what makes it true?
    ... >> entity in ZFC without introducing any new inconsistency. ... >> consistent statement asserting the existence of a natural number ... opaquely invoke the Axiom of Infinity to assert the existence of N, ... PA allow 'natural numbers' that are *not* modelled by finite ordinals. ...
    (sci.math)
  • Re: an important set theory post
    ... existence of cardinals but not the existence of ... But the alephs are indexed by ... mentioning ordinals. ...
    (sci.math)