Cardinal Zero is Less than Cardinal One
- $0 < 1$
We have that the Cardinals are Totally Ordered.
Let $\RR \subseteq \O \times \set \O$ be any arbitrary relation between $\O$ and $\set \O$.
Thus by definition, $\RR$ is in fact a mapping.
So, by definition, $\set \O$ dominates $\O$.
Since Empty Set is Subset of All Sets, we have $\O \subseteq \set \O$.
Hence the result.