Floor Function/Examples/Floor of Root 2

Theorem

 * $\floor {\sqrt 2} = 1$

where $\floor x$ denotes the floor of $x$.

Proof
The decimal expansion of $\sqrt 2$ is:
 * $\sqrt 2 \approx 1.41421 \ 35623 \ 73095 \ 0488 \ldots$

Thus:
 * $1 \le \sqrt 2 < 2$

Hence $1$ is the floor of $\sqrt 2$ by definition.