leq

Represents a less-than-or-equal-to relationship between mathematical expressions or values.

Overview

Essential for expressing mathematical inequalities and constraints across various disciplines, particularly in algebra, analysis, and optimization theory.

Commonly used in mathematical proofs and theorem statements
Appears frequently in set theory to define subsets and ordering relationships
Critical in programming and computer science for expressing logical conditions
Found extensively in optimization problems when defining constraints or bounds

Examples

Expressing a basic inequality with less than or equal to.

x \leq 5

x \leq 5

Defining a range or interval with both endpoints included.

0 \leq x \leq 1

0 \leq x \leq 1

Comparing a sequence term to its limit.

a_n \leq L \text{ for all } n \in \mathbb{N}

a_n \leq L \text{ for all } n \in \mathbb{N}