Definition:Ceiling Function/Definition 2

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