Re: Cantor Confusion

In article <1163154101.329683.20480@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:

William Hughes schrieb:


If it is not a member, then A' has one member less than the otherwise
same set A where it is a member. Therefore A and A' are different,
aren't they?


Completely irrelevent. The bijection is not between one set without
supremum
and this set plus supremem. The fact that there are aleph_0 terms in
the first column, does not mean there is an aleph_0 th line.

What makes up the difference to the fact that there are not aleph_0
terms in any line?
Or is there no difference between aleph_0 terms and less than aleph_0
terms?

Not if the "difference" is finite.


Remember,
the fact that there are infinitely many lines does not mean
that ther is a line with index aleph_0.

The column has infinitely many indexes. No line has infinitely many
indexes. No difference?

Not significant in comparing the number of lines, when the line lengths
are unbounded to the number of columns.

Lines with finitely many indexes cannot exhaust the column with its
infinitely many. We learn: Infinity cannot be exausted.

Infinite sets CAN be exhausted, but only by infinite processes.

WM's problem is that he does not, perhaps cannot, understand that there
is a difference in the way infinite sets and infinite processes work
from the way that finite sets and finite processes work.

Getting over than hurdle is one of the major problems that all beginning
calculus students must face and conquer. WM has not yet done so.
.

Quantcast