Set Theory and Logic

    

The Continuum Theorem

Authors: David L. Selke

An injection from omega-1 to the paths in the binary tree leads to a bijection between the omega-length binary strings and an aleph-1 sized set. Since there are 2^aleph-null many omega-length binary strings, this proves the Continuum Hypothesis, 2^aleph-null = aleph-1. The technique may be extended to show the Generalized Continuum Hypothesis, which however will be reported separately.

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[v1] 2024-02-06 20:56:59

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