Re: *** T. Winter says: Definition: sum{i in N} i = 0

On Sun, 10 Jun 2007 14:32:56 -0600, Virgil <virgil@xxxxxxxxxxx>
wrote:

Let's consider the following infinite list:

1
11
111
.
.
.


The diagonal cannot be longer than every line, because it consists
of line elements. [WM]


Mückenheim's World is a fascinating place (if you are insane).

Q: How long is the list, how many lines does it have?

A: It's infinitely long, it has infinitely many lines.

Q: Right. How many diagonal elements are there (then)?

A: Well, in this case there are infinitely many diagonal elements,
since in every line of the list there is a diagonal element.

Q: Right. Means?

A: The diagonal is infinitely long.

Q: Right. And how long are the lines in the list - how many digits
do they have?

A: Well, they _all_ are finite, hence they _all_ have (only)
finitely many digits.

Q: Means?

A: The diagonal is longer than each and any line in the list.

WM: But the diagonal cannot be longer than every line, because it
consists of line elements.

Q: Well.

A: Well.


F.

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