Re: Cantor Confusion

mueckenh@xxxxxxxxxxxxxxxxx wrote:
MoeBlee schrieb:

David Marcus wrote:
Obviously, I could be wrong, but I think WM means map it on a line of
the list. He seems to think that because we construct the diagonal from
the list, the diagonal must be one of the lines in the list. Why he
thinks this, I have no clue.

You mean map the diagonal (or the range of the diagonal, or whatever)
onto one of the finite sequences that is in the range of the infinite
sequence of those finite sequences? I.e., map the diagonal onto a
member of the range of S? A 1-1 map? If so, yes, I would share your
bafflement as to why we should think there is such a mapping or what
contradiction there is in there not being such a mapping.

There is a mapping of the diagonal on a (each) column.

Okay, if you want to put it that way.

There is no mapping of the diagonal on any line.

Okay.

The diagonal cannot have more elements than the width of the matrix is.

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.
If you don't define 'the width', then 'the width' is empty language and
is irrelevent.

The number of elements of the diagonal is assumed to be omega.
That is wrong, because only the supremum is omega.

I answered that already. And the cardinality of the diagonal is not
assumed, but is proven, to be omega. And the fact that omega is a limit
ordinal greater than any finite segment of the diagonal is not in
contradiction with anything in the proof nor does it entail that the
cardinality of the diagonal cannot be omega.

So, at this point, you have just returned with replies that I've
already answered, and you haven't shown any step in my proof tha is not
justified by first order logic applied to the Z axioms nor have you
shown a sentence P and ~P of the language of set theory such that both
are theorems of set theory.

MoeBlee

.

Relevant Pages

  • Re: Cantor Confusion
    ... You mean map the diagonal ... onto one of the finite sequences that is in the range of the infinite ... contradiction there is in there not being such a mapping. ... The number of elements of the diagonal is assumed to be omega. ...
    (sci.math)
  • Re: Cantor Confusion
    ... You mean map the diagonal ... onto one of the finite sequences that is in the range of the infinite ... contradiction there is in there not being such a mapping. ... because only the supremum is omega. ...
    (sci.math)
  • Re: Cantor Confusion
    ... David Marcus wrote: ... You mean map the diagonal ... onto one of the finite sequences that is in the range of the infinite ... contradiction there is in there not being such a mapping. ...
    (sci.math)
  • Re: Models of the theory of Categories
    ... and the other an operator-preserving map from the elements of ... what you have is a category of algebras ... of type Omega, and a second category of algebras of type Omega', ... ; Rings with unity as ...
    (sci.math)
  • Re: Review of Mueckenheims book.
    ... omega is a mapping from omega into the power set of omega. ... While the mapping from omega to its power set in which each element is ... "identity function" to a mapping which clearly is not of this form. ...
    (sci.math)