Re: Relative Cardinality



Virgil wrote:
> In article <1121530089.812104.106490@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
> mueckenh@xxxxxxxxxxxxxxxxx wrote:
>
> > Randy Poe wrote:
> > > mueckenh@xxxxxxxxxxxxxxxxx wrote:
> > > > This is a requirement to satisfy the principle. The principle reads:
> > > > You must be able to compare an existing real number with any other
> > > > existing real number with the result that one of them is larger or both
> > > > are equal.
> > >
> > > No, the axiom you are thinking of says that if a and b are
> > > members of the set of reals, then either a = b, a < b, or a > b.
> > > Exactly one of those must be true.
> >
> > Correct. And if it cannot and nevrr be determined which case is given,
> > then at least one of the numbers a and b is not a real number.
>
> The rule says one and only one is true, it does not ever say that there
> must be some method available to determine that truth. And in general,
> not everything that is true must be known to be true.
> >
> > The axioms are valid in mathematics. What should axioms be good for if
> > they did not apply?
>
> What axiom says that there must be a METHOD for determining which of
> a = b, a < b, or a > b is true?

If a and b are real numbers, then one of the three relations holds. If
there is no method to find out which one it is, then we cannot prove
which one of the relations holds. That means we cannot prove that one
of them is true. That implies that a or b or both are not real numbers.

But it is uninteresting to further discuss this if you want to believe
in things we can never know. Stay with your matheology erroneously
called mathematics. I want to propagate the truth but not to convince
by any means. If you are not willing to exchange truth for your false
belief than further talking is useless.

Regards, WM

.

Relevant Pages

  • Re: Godel did not destroy the Hilbert Frege Russell programme
    ... formally undecidable propositions of Principia Mathematica and related ... the axiom of infinity to PM, in the form "there exist denumerably many ... recursive subset of the set of well-formed formulas  of the language ... truth values, such that, for all valuations v of S, the truth- ...
    (sci.logic)
  • Re: Godel did not destroy the Hilbert Frege Russell programme
    ... formally undecidable propositions of Principia Mathematica and related ... the axiom of infinity to PM, in the form "there exist denumerably many ... recursive subset of the set of well-formed formulas  of the language ... truth values, such that, for all valuations v of S, the truth- ...
    (sci.logic)
  • Re: (OT) Re: Godel
    ... In real life truth is much less absolute. ... about Truth end up retreating in mathematics where truth can be absolutely ... controlled -- after all, you decide on the axioms and rules of deduction, hey? ... that reject the axiom of choice altogether, ...
    (Debian-User)
  • Re: Godel did not destroy the Hilbert Frege Russell programme
    ... formally undecidable propositions of Principia Mathematica and related ... the axiom of infinity to PM, in the form "there exist denumerably many ... recursive subset of the set of well-formed formulas  of the language ... truth values, such that, for all valuations v of S, the truth- ...
    (sci.logic)
  • Re: I dont like the Axiom of Choice
    ... And this is what the Axiom of Choice is doing - making claims without ... Throughout most of my mathematics education, ... truth, or just accepted to be truth as a foundation point. ...
    (sci.math)
Quantcast