The Continuum is Countable: Infinity is Unique

Details The Continuum is Countable: Infinity is Unique The Continuum is Countable: Infinity is Unique

2008-09-24

arxiv.org/abs/0809.4144v1

Mathematics

General Mathematics

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Scientific paper

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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