Re: Cantor Confusion

In article <1162828907.384237.5300@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:

Virgil schrieb:

In article <1162563567.735020.246810@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:

Virgil schrieb:

In article <1162470874.593282.36250@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:

WM merely repeated his automatic error several more times here.

WM claims that a list in which the nth listed element is a string of
length at least n characters cannot produce a diagonal of length
greater that any finite number of characters.


The diagonal needs an element from every line, the n-th element from
the n-th line. Therefore it cannot be longer than every line.

The "diagonal"must be longer than every finite "line".

But it cant, because each of its elements stems from a line.

Which line(s) is the diagonal NOT longer than when line n is at least of
length n?

The only way it
will ever fail to be longer than some "line" is if that line is itself
infiitely long.

Which is impossible, because each of its elements stems from a line.

When for all n in N, line n is of length n, which is quite possible,
then for all n in N, the diagonal is of length >= n.

That looks like an infinite diagonal to me.

WM is assuming that since every natural is finite, there must be a
largest natural, but in ZF and NBG, that is specifically false.

And no assumptions, however hidden, by WM can make it otherwise.
.

Relevant Pages

  • Re: Cantor Confusion
    ... WM merely repeated his automatic error several more times here. ... greater that any finite number of characters. ... The diagonal needs an element from every line, ... will ever fail to be longer than some "line" is if that line is itself ...
    (sci.math)
  • Re: Cantor Confusion
    ... WM claims that a list in which the nth listed element is a string of ... greater that any finite number of characters. ... The diagonal needs an element from every line, ... because each of its elements stems from a line. ...
    (sci.math)
  • Re: Cantor Confusion
    ... WM merely repeated his automatic error several more times here. ... WM claims that a list in which the nth listed element is a string of ... greater that any finite number of characters. ... The diagonal needs an element from every line, ...
    (sci.math)
  • Re: Cantor Confusion
    ... Virgil schrieb: ... WM merely repeated his automatic error several more times here. ... WM claims that a list in which the nth listed element is a string of ... greater that any finite number of characters. ...
    (sci.math)
Quantcast