Re: Cantor Confusion

In article <1162986270.218701.275100@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:

MoeBlee schrieb:

I answered that already. If you define 'the width', then it turns out
to be equal to omega, which is just what the length of the diagonal is.

The diagonal is assumed to exist such that each of its digits exists,
actually. This is established by the mapping on a column. But it cannot
be established by the mapping on any line.

Why should the diagonal have to be mapped onto one line when it is not
constructed from one line?

WM seem to have all sorts of peculiar requirements for things that need
not be required for anything except his own squirrelly views of things.





I answered that already. And the cardinality of the diagonal is not
assumed, but is proven, to be omega.

It is *assumed* by stating the axiom of infinity. Without this
assumption the length was not omega.

The axiom of infinity has not been shown to cause any problems within ZF
or NBG, and WM has not produced any /system/ in which it does not hold.
.

Relevant Pages

  • Re: Why? [was Re: Cantor`s powerset theorem is false?]
    ... Suppose, for an arbitrary n in omega, n not in n. ... you said that we are considering ZF without the power set axiom and ... axiom of infinity ... Then we have an inconsistent theory, since N u would be a universal ...
    (sci.logic)
  • Re: Why? [was Re: Cantor`s powerset theorem is false?]
    ... The axiom of infinity states that there is a set closed under the ... simply that of having a bijection with omega or with a member of omega. ...
    (sci.logic)
  • Re: Why? [was Re: Cantor`s powerset theorem is false?]
    ... The axiom of infinity ALREADY says and does that. ... that omega does not belong to omega is equivalent to asserting the ... That the successor of EACH AND EVERY ...
    (sci.logic)
  • Re: Cantor Confusion
    ... Only in WM's world is omega itself needed to make things not finite. ... axiom of infinity, because that guarantees that you can even talk about ...
    (sci.math)
  • Re: An uncountable countable set
    ... >> Let us remove omega from that set. ... What is the resulting cardinality? ... Without omega there is no actual infinity. ... If there are infinitely many naturals ...
    (sci.math)