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Topic: Matheology § 240
Replies: 36   Last Post: Apr 12, 2013 7:15 PM

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 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
Matheology § 240
Posted: Apr 7, 2013 4:24 AM

Matheology § 240

Consider a Cantor-list that contains a complete sequence (q_k) of all
rational numbers q_k. The first n digits of the anti-diagonal d are
d_1, d_2, d_3, ..., d_n. It can be shown *for every n* that the Cantor-
list beyond line n contains infinitely many rational numbers q_k that
have the same sequence of first n digits as the anti-diagonal d.

Proof: There are infinitely many rationals q_k with this property. All
are in the list by definition. At most n of them are in the first n
lines of the list. Infinitely many must exist in the remaining part of
the list. So we have obtained:

For all n exists k: d_1, d_2, d_3, ..., d_n = q_k1, q_k2, q_k3, ...,
q_kn.
This theorem it is not less important than Cantor's theorem: For all
k: d =/= q_k.

Both theorems contradict each other with the result that finished
infinity as presumed for transfinite set theory is not a valid
mathematical notion.

Regards, WM

Date Subject Author
4/7/13 mueckenh@rz.fh-augsburg.de
4/7/13 fom
4/7/13 mueckenh@rz.fh-augsburg.de
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4/7/13 Virgil
4/8/13 mueckenh@rz.fh-augsburg.de
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4/7/13 Virgil
4/7/13 Virgil
4/7/13 mueckenh@rz.fh-augsburg.de
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4/8/13 mueckenh@rz.fh-augsburg.de
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4/8/13 fom
4/9/13 fom
4/9/13 mueckenh@rz.fh-augsburg.de
4/9/13 Virgil
4/10/13 mueckenh@rz.fh-augsburg.de
4/10/13 Virgil
4/12/13 mueckenh@rz.fh-augsburg.de
4/12/13 fom
4/12/13 fom
4/12/13 Virgil
4/7/13 Virgil
4/7/13 Virgil
4/7/13 mueckenh@rz.fh-augsburg.de
4/7/13 Virgil
4/7/13 Virgil