Set Theory and Logic

    

Equality Hypothesis in Diagonal Argument

Authors: Hongyi Li

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.

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[v1] 2024-01-07 21:10:16

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