Re: Cantor Confusion


William Hughes schrieb:



Given that you find the words function, and bijection so
distasteful, I have reworked my points to avoid using
them in conection with potentially infinite sets.
Please stop me at the first point you disagree with.

[...]

-given two sets of natural numbers E and F where E is a
potentially
infinite set, and F has a largest element. there does
not exist an equitransform between E and F


Until here all is correct, as far as I see.

-the diagonal is the potentially infinite set of natural
numbers.

-every line L has a largest element

-there is no equitransform between the diagonal and a line L

And here we have the contradiction:

1) The set of lines is also the potentially infinite set of natural
numbers.
2) Every element of the diagonal is in at least one line.
3) Every initial segment of the diagonal is (in) a line.
4) The limit (n -->oo, for the number n of elements) of the diagonal is
oo.
5) The limit (m -->oo, for the number m of elements of a line) is less
than infinite.
6) Therefore not every initial segment of the diagonal can be (in) a
line.
7) Contradiction between (3) an (6).

Regards, WM

.

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