lessthan

Lessthan, commonly referred to as the less-than relation, is a fundamental comparison that expresses that one quantity is strictly smaller than another. It is typically written with the symbol <, and is defined on any totally ordered set, such as the real numbers, integers, or strings under lexicographic order in some contexts. The assertion a < b means that a is strictly less than b, with no possibility of equality.

Mathematically, < is irreflexive (a < a is false) and transitive (if a < b and b < c then a < c). In a totally ordered domain, every pair of elements is comparable, and for any a ≠ b, exactly one of a < b or b < a holds.

In computing, the less-than operator < is a binary comparison that yields a boolean result. It is primarily used for numeric comparisons, but in many languages it also applies to strings via lexicographic ordering, or to other objects via user-defined ordering. Some floating-point environments follow IEEE 754 and treat comparisons with NaN as false.

Common uses include conditional branching, loops, and data filtering, as in selecting elements with x < 10 or sorting data in ascending order. The strict form (<) is contrasted with less-than-or-equal (≤), which allows equality.

The concept of lessthan is foundational across mathematics and computer science, underpinning inequality reasoning, algorithm design, and data processing.