Re: Galileo's Paradox and the Project of the Reals

Tony Orlow wrote:
Mike Kelly wrote:
Tony Orlow wrote:
David Marcus wrote:
Tony Orlow wrote:
David Marcus wrote:

You haven't noticed that Tony is a crank? And, that what he wrote above
is vague nonsense?
I'd rather be a crank than a cog, or a stick in the mud, David.
Then I guess you've got your wish. Tell me: are you incapable of
learning math or do you choose not to?

I choose not to accept nonsense conclusions justified by unsound axioms,
if that's what you mean...

Which axioms would those be?

Take the axiom of infinity, for instance. It declares an infinite "set",
but it cannot do so with just the notion of set membership, so it
inserts Peano's successor relation as well.

Please state the axiom of infinity that you are discussing.

--
David Marcus
.

Relevant Pages

  • 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)
  • Re: Logarithm of transfinite numbers
    ... These infinity arguments always seem to boil down to ... standard models vs non-standard models. ... Peano's axioms are model blind: ...
    (sci.math)