Definition:Ceiling Function/Definition 1
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Definition
Let $x$ be a real number.
The ceiling function of $x$ is defined as the infimum of the set of integers no smaller than $x$:
- $\ceiling x := \inf \set {m \in \Z: x \le m}$
where $\le$ is the usual ordering on the real numbers.
Also known as
The ceiling function is also known as the least integer function or lowest integer function.
Also see
Theorems used in this definition:
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