Re: abundance of irrationals!) - rectangles of area 1.bmp [0/1]



Virgil said:
> In article <MPG.1cea7e1a9c12de61989bf2@xxxxxxxxxxxxxxxxxxxxxxxxx>,
> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
>
>
> > >
> > > > I have provided two proofs. Counting WILL NOT get you to infinity. It's
> > > > a weak tool for trying to study infinty. It's fine for finite things.
>
> But the axiom of infinity and the principle of induction do get you to
> infinity in finitely many steps. That is what they are for.
> > >
> > > Indeed. Except that your proofs have been refuted thoroughly.
>
> > Not in any way that doesn't refute the proofs you hold so dear, and
> > not in any substantive way. Only by retreating to your local set of
> > confusions in the form of unquestionable contradictory axioms and
> > assumptions do you parry your away out of truth's way.
>
> Without some set of axioms as a foundation, there is no truth, only
> chaos. The axioms WE use have been tested and not found wanting. The
> informal unaxiomatized logic you are trying to use has been also tested
> and has been found wanting. So any contradictions are in your arena, not
> ours.
>
They haven't been tested very well. I have detected several inconsistencies, so
I don't know what people have been looking at. I don't know exactly what is
wrong with mathematics in the last century, but there is pervasive insanity in
this area that needs correction. You are wrong. Comment on my set size method,
or shut up.
--
Smiles,

Tony
.



Relevant Pages

  • Re: abundance of irrationals!) - rectangles of area 1.bmp [0/1]
    ... Counting WILL NOT get you to infinity. ... Without some set of axioms as a foundation, there is no truth, only ... The axioms WE use have been tested and not found wanting. ...
    (sci.math)
  • Re: infinitely many nns = infinite nns?
    ... First, you would have to STATE SOME AXIOMS, ... Here, "infinitely many" is aleph-0, which is "actual infinity." ... Similarly, the "fact" that all the numbers are "finite" means that all numbers have values LESS THAN aleph-0, that the natural numbers are limited to "potentially infinite" values. ... To be honest, it won't SURPRISE me one iota if you claim that there are some natural numbers with infinitely many digits, but that they, too, have only finite values. ...
    (sci.logic)
  • Re: infinitely many nns = infinite nns?
    ... You asked for my axioms, and I really want to use the standard ones, so the question is mostly pointless, but I thought I would give clearer definitions of how I am using actual and potential infinity. ... "Aleph-0" DOES NOT EXIST outside some LOGICAL context ... "Actual infinity" is a term from informal natural-language ...
    (sci.logic)
  • Re: infinitely many nns = infinite nns?
    ... These are axioms and assumed correct. ... state whether they should be used with potential, or actual, infinity. ... cannot use potential infinity for some conclusions, ... through Axiom, mathematical induction, or as it is sometimes called, ...
    (sci.logic)
  • Re: Existence of reals and observation of them
    ... infinity, then infinity doesn't exist even as cardinality. ... You need to read the axioms and the derivations of the theorems ... if persons of good will could continue to disagree over basic ... science of mathematics. ...
    (sci.math)

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