Set Theory and Logic

The Continuum Theorem II

Authors: David Selke
Comments: 8 Pages.

An injection from the countable ordinals to the paths in the binary tree leads to a bijection between all paths in the binary tree and only those in the $aleph_1$-sized injection. Since there are $2^{aleph_0}$ many paths in the binary tree, this proves the Continuum Hypothesis, $2^{aleph_0} = aleph_1$.
Category: Set Theory and Logic