Ceiling Function/Examples/Ceiling of Root 2

Theorem

 * $\left\lceil{\sqrt 2}\right\rceil = 2$

where $\left\lceil{x}\right\rceil$ denotes the ceiling of $x$.

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

Thus:
 * $2 \ge \sqrt 2$

and:
 * $1 < \sqrt 2$

Hence $2$ is the ceiling of $\sqrt 2$ by definition.