Ceiling Function

Floor and ceiling functions

Say we have $\alpha$, then $\lfloor\alpha\rfloor$ is the greatest integer less than or equal to $\alpha$ and $\lceil\alpha\rceil$ is the smallest integer greater than or equal to $\alpha$. Finally, $\{ \alpha \}$, the fractional part of $\alpha$, is the part of the real number $\alpha$ after the decimal.