Vocabulary - Ceiling

The ceiling function $\lceil x \rceil$ rounds $x$ up to the nearest integer. For example, $\lceil 7.1 \rceil = 8$ and $\lceil -2.9 \rceil = -2$ (up means toward positive infinity).

You use ceiling when you need to know how many groups are required to hold all items. If you have $7$ items and each group holds $3$, you need $\lceil 7 / 3 \rceil = 3$ groups.

A trick: $\lceil a / b \rceil = \lfloor (a + b - 1) / b \rfloor$ when $a$ and $b$ are positive integers. This avoids floating-point division.