Re: infinity ...

David R Tribble wrote:
> Albrecht S. Storz wrote:
> > [...]
> > Since there is no biggest number and since there is no infinite number,
> > the size of the set of numbers in form of sets of #s is undefined as
> > the biggest natural number is undefined.
> >
> > But the sequence of the sets of # fullfill the peano axiomes. So this
> > set must be infinite.
> >
> > The cardinality of a set is not able to be infinite and "not defined"
> > at the same time.
> > This is the contradiction.
>
> I don't see the contradiction. The size of the set is "not defined"
> to be the same as any natural number, and the set size is obviously
> infinite. This is no contradiction, since no natural number is
> infinite.
>
> The thing that is "not defined" is the largest natural, which obviously
> does not exist. But the set size is infinite, and is nicely defined
> by an infinite cardinal.
>
> You seem to be mixing the two concepts of "natural" and "cardinal"
> numbers to create a supposed contradiction, but that does not work.


You are not able to understand that there is no difference between
numerals and sets. My sketches shows this exactly.
Cantor proofs his wrong conclusion with the same mix of potential
infinity and actual infinity. But there is no bijection between this
two concepts. The antidiagonal is an unicorn.
There is no stringend concept about infinity. And there is no aleph_1,
aleph_2, ... or any other infinity.

Regards

AS

.

Relevant Pages

  • Re: new standard for Euclid IP proof-- able to give both Direct and Indirect alongside one a
    ... By contradiction: ... Mark I can understand now why you like the Wikipedia entry even though ... cardinality increase from any finite cardinality ... *any* finite set is increased in cardinality implies it is infinite. ...
    (sci.math)
  • Re: infinity
    ... >>> Empty words, no reasoning. ... > any concatenation of all the words in it. ... >> finite, then there are NO infinite lengths, and the sum can NEVER be ... this contradiction derives from the contradiction of the largest finite, ...
    (sci.math)
  • Re: infinity
    ... >>> The only contradiction arises from your obsession with a last ... >> you mean by infinite. ... and without any upper bound. ... A rough estimate of the number of atoms making up Earth can be made, ...
    (sci.math)
  • Re: infinity
    ... You cannot pin down the largest finite natural, ... You have declared that the size of the set of finite naturals ... > is infinite, and all elements are finite, which is a contradiction. ...
    (sci.math)
  • Re: infinity
    ... >> of 'infinite' is wrong? ... > set of naturals as defined by Peano is therefore infinite, ... you insist there is some contradiction. ... When talking about lists of positive integers, ...
    (sci.math)
Quantcast