Set Theory and Logic

2401 Submissions

[2] viXra:2401.0116 [pdf] replaced on 2024-01-31 17:28:42

First Case of Mistake in Cantor’s Proof: Pure Double Contradiction Technique

Authors: Juan Carlos Caso Alonso
Comments: 39 Pages.

The proof of Cantor's Theorem ( |A| < |P(A)| ), changes depending to which mathematician you ask. There are two versions of it. The one I call "Creating an extern element", and the other one I call "Pure double contradiction".This document will try to explain the difference between them, and after that show that the second one should not be never used, for being "not reliable".In case you are interested, you have an extra chapter, with informal data about the first one.
Category: Set Theory and Logic

[1] viXra:2401.0042 [pdf] submitted on 2024-01-07 21:10:16

Equality Hypothesis in Diagonal Argument

Authors: Hongyi Li
Comments: 5 Pages.

In the Diagonal Argument, there are two independent hypotheses, the countability hypothesis and the equality hypothesis, which violate the basic principle of proof by contradiction, so the Diagonal Argument cannot be held. Closer analysis shows that the Diagonal Argument only falsifies the equality hypothesis and has nothing to do with the countability hypothesis. Since the equality hypothesis is inherently wrong and does not need to be falsified at all, the Diagonal Argument actually proves nothing. The transfinite number theory and Continuum hypothesis therefore become meaningless. Once again calls on the education department to suspend the teaching of infinite sets, so as not to mislead people.
Category: Set Theory and Logic