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arXiv:0809.4144math.GM

The Continuum is Countable: Infinity is Unique

Laurent Germain

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Abstract

Since the theory developed by Georg Cantor, mathematicians have taken a sharp interest in the sizes of infinite sets. We know that the set of integers is infinitely countable and that its cardinality is Aleph0. Cantor proved in 1891 with the diagonal argument that the set of real numbers is uncountable and that there cannot be any bijection between integers and real numbers. Cantor states in particular the Continuum Hypothesis. In this paper, I show that the cardinality of the set of real numbers is the same as the set of integers. I show also that there is only one dimension for infinite sets, Aleph.

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math.GMGeneral Mathematics

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  1. P might be NP: A Polynomial Time Algorithm for the Hamilton Circuit Problem 1 comment

    • Fair enough, but people should know that arXiv does not have a crackpot filter (this is not a bad thing. ArXiv is excellent!) Any random pdf claiming to decide P = NP on the internet is going to be crackpot stuff. (Off topic) My favourite silly arXiv post is this one, mostly for…

      jacobparkerView on HNParent context

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