The ceiling function is a mathematical function that associates with any real number $x$ the smallest integer $n$ such that $n \geq x$, and is often noted as $\lceil x \rceil$ or $\operatorname{ceil}(x)$. In other words, the ceiling of $x$ is the smallest integer greater than or equal to $x$.

LaTeX Code

The ceil function can be easily implemented in LaTeX using the following command:

$$\lceil x \rceil$$
\[\lceil x \rceil\]

Ceil Function

The ceil function is formally defined as:

$$\lceil x \rceil = \operatorname{min}\{n \in \mathbb{Z} : n \geq x\}$$
\[\lceil x \rceil = \operatorname{min}\{n \in \mathbb{Z} : n \geq x\}\]

Example of Use

Suppose we want to round the number $x=4.7$ up to the nearest integer. We can use the $\lceil x \rceil$ function, which returns the smallest integer greater than or equal to $x$. In this case, we have:

$$\lceil 4.7 \rceil = 5$$
\[\lceil 4.7 \rceil = 5\]