lessthanorequal

Lessthanorequal, often written as the symbol ≤, denotes the relation of being not greater than between two quantities. In mathematics, x ≤ y means that x is less than or equal to y. This relation is used on ordered sets such as the real numbers, integers, and rationals, and generalizes to any set equipped with a comparable order.

As a binary relation on an ordered set, ≤ is reflexive (a ≤ a for all a), antisymmetric (if a ≤ b and b ≤ a then a = b), and transitive (if a ≤ b and b ≤ c then a ≤ c). On the real numbers, ≤ is a total order: for any a and b, either a ≤ b or b ≤ a (or both when a = b).

In mathematics, ≤ is used to compare sizes, define intervals [a, b], describe convergence and monotonicity, and formulate inequalities that bound quantities. In computer science, ≤ appears as a comparison operator in many programming languages, often written with the same symbol ≤ or as <= in ASCII form; it returns a boolean indicating whether the left operand does not exceed the right. The phrase less than or equal to is also used in natural language and in name or identifier conventions, such as function or variable names that encode the operator's meaning, sometimes rendered as lessthanorequal in code documentation.