Floor Function/Examples/Floor of Root 2

Theorem

 * $\left\lfloor{\sqrt 2}\right\rfloor = 1$

where $\left\lfloor{x}\right\rfloor$ denotes the floor of $x$.

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

Thus:
 * $1 \le \sqrt 2$

and:
 * $2 > \sqrt 2$

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