Definition:Ceiling Function/Definition 2

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Let $x \in \R$ be a real number.

The ceiling function of $x$, denoted $\ceiling x$, is defined as the smallest element of the set of integers:

$\set {m \in \Z: x \le m}$

where $\le$ is the usual ordering on the real numbers.

Also known as

The ceiling function is also known as the least integer function.

Also see

Technical Note

The $\LaTeX$ code for \(\ceiling {x}\) is \ceiling {x} .

When the argument is a single character, it is usual to omit the braces:

\ceiling x