Ceiling function

Definition

Let $x$ be a real number. The ceiling of $x$, written $\lceil x \rceil$, is the least integer $n$ with $x \le n$. The ceiling function is the function $\mathbb{R} \to \mathbb{Z}$, $x \mapsto \lceil x \rceil$.

Remarks

The ceiling and the floor are related by $\lceil x \rceil = -\lfloor -x \rfloor$. For each real $x$, $x \le \lceil x \rceil < x + 1$. If $x$ is not an integer, then $\lceil x \rceil = \lfloor x \rfloor + 1$. If $x$ is an integer, then $\lceil x \rceil = \lfloor x \rfloor = x$.

Explanations

L1 human

The ceiling of a number rounds it up to a whole number. If a trip needs $2.1$ buses, then you must order $\lceil 2.1 \rceil = 3$ buses.