Re: Cantor Confusion


mueckenh@xxxxxxxxxxxxxxxxx wrote:
Virgil schrieb:

(It is contained in the union of all lines, but the
union of all lines is not a line)

That is a void assertion unless you can prove it by showing that
element by which the union differes from all the lines.

Not quite. In order to achieve that the diagoal is not in any linem all
that is required is:
Given any line there is an element of the diagonal not in THAT line.
It is not requires that:
There is an element of the diagonal that is not in any line.


For linear sets you cannot help yourself by stating that the diagonal
differs form line A by element b and from line B by element a, but a is
in A and b is in B. This outcome is wrong.

Therefore your reasoning "there is an element of the diagonal not in
THAT line. It is not required that: There is an element of the diagonal
that is not in any line." is inapplicable for linear sets. You see it
best if you try to give an example using a finite element a or b.


In every finite example the line that contains
the diagonal is the last line.

Your claim is that there is a line which contains the diagonal.
Call it L_D. Question: "Is L_D the last line?"

- William Hughes

.

Relevant Pages

  • Re: Cantor Confusion
    ... element by which the union differes from all the lines. ... For linear sets you cannot help yourself by stating that the diagonal ... so the antecedent cannot be true. ...
    (sci.math)
  • Re: Cantor Confusion
    ... element by which the union differes from all the lines. ... For linear sets you cannot help yourself by stating that the diagonal ... Every element that can be shown to belong to the diagonal can be shown ...
    (sci.math)
  • Re: Cantor Confusion
    ... That is a void assertion unless you can prove it by showing that ... element by which the union differes from all the lines. ... For linear sets you cannot help yourself by stating that the diagonal ...
    (sci.math)
  • Re: Cantor Confusion
    ... element by which the union differes from all the lines. ... For linear sets you cannot help yourself by stating that the diagonal ... infinite segment in the diagonal, then it is not in a line. ...
    (sci.math)
  • Re: Cantor Confusion
    ... That is a void assertion unless you can prove it by showing that ... element by which the union differes from all the lines. ... For linear sets you cannot help yourself by stating that the diagonal ...
    (sci.math)
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