Definition:Ceiling Function/Definition 2
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Definition
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 or lowest integer function.
Also see
- Set of Integers Bounded Below by Real Number has Smallest Element
- Smallest Element is Unique
- Equivalence of Definitions of Ceiling Function
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
Sources
- 1977: Gary Chartrand: Introductory Graph Theory ... (previous) ... (next): Chapter $2$: Elementary Concepts of Graph Theory: $\S 2.2$: Isomorphic Graphs
- 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.4$: Integer Functions and Elementary Number Theory
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): integer part
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): integer part