nonequal

Nonequal is an adjective used to describe a relationship or state in which two values, objects, or quantities do not share the same value. In mathematics and logic, the standard phrase is "not equal to," commonly represented by the symbol ≠. The nonequal relation consists of all ordered pairs (a, b) where a differs from b. It is the complement of equality, is irreflexive (a ≠ a is false), and is symmetric (if a ≠ b, then b ≠ a), but it is not in general transitive.

In programming and computing, explicit nonequal operators are widely used. Languages such as C, C++, Java, and Python typically use != to test that two expressions have different values, while some SQL dialects historically use <>. These operators return true when the operands differ and false when they are the same. In data analysis and database queries, checking for nonequal values is a routine step in filtering, conditional logic, and join operations.

Usage notes indicate that nonequal is a descriptive, but relatively uncommon, single-word form. More standard and widely understood terms are "not equal" and "unequal." The choice of wording can affect readability, and many style guides prefer the two-word form in formal writing.

See also: inequality, not equal to, equality, ≠ operator.