Power Set is Nonempty

Theorem

Let $S$ be a set.

Then:

$\powerset S \ne \O$

Proof

By Empty Set is Element of Power Set:

$\O \in \powerset S$

Thus we conclude that $\powerset S$ is non-empty.

$\blacksquare$

This article is issued from ProofWiki. The text is available under Creative Commons Attribution-ShareAlike License unless otherwise noted. Additional terms may apply for the media files.