Re: Cantor Confusion


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.
There is no mapping of the diagonal on any line.
The diagonal cannot have more elements than the width of the matrix is.

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

Regards, WM

Regards, WM

.

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