lceil

Represents the left ceiling bracket used for denoting the ceiling function in mathematics, which rounds numbers up to the nearest integer.

Overview

Essential in discrete mathematics and computer science for expressing the ceiling operation, which maps a real number to the smallest following integer.

Commonly paired with \rceil to enclose expressions
Frequently used in algorithmic complexity analysis
Appears in number theory and computational problems
Important in probability theory for expressing discrete bounds
Often encountered in programming-related mathematical notation

Examples

Rounding up a real number to the nearest integer (ceiling function).

\lceil \pi \rceil = 4

\lceil \pi \rceil = 4

Computing the number of groups needed when dividing n items into groups of size k.

\text{Groups needed} = \left\lceil \frac{n}{k} \right\rceil

\text{Groups needed} = \left\lceil \frac{n}{k} \right\rceil

Expressing the upper bound of a logarithmic complexity.

\text{Space complexity} = \lceil \log_2(n) \rceil \text{ bits}

\text{Space complexity} = \lceil \log_2(n) \rceil \text{ bits}