min3

Min3 refers to the minimum of three values. In mathematics and computer science, min3 denotes the smallest element among a, b, and c. It can be written as min(a,b,c) and is classically defined as min(a,b,c) = min(min(a,b), c), since the minimum over a finite set can be obtained by successive comparisons.

As a function, min3 is commutative in its inputs and associative in the sense that the order of comparisons does not affect the final result. The result is the smallest of the three arguments; if some values are equal, the shared minimum is returned.

Examples include: min3(5, 2, 9) = 2; min3(-7, 3, -1) = -7; min3(4, 4, 2) = 2.

In programming contexts, min3 is often implemented as a three-argument variant of the two-argument min function, for instance min(min(a,b), c). It is useful in simple filtering, clamping operations, or when maintaining a running best value over a fixed-size window.

Variants and related concepts include the minimum of more than three numbers and the median of three, which is a different statistic that depends on the middle value rather than the smallest. Some libraries or codebases may name a three-argument minimum function as min3, min4, etc., or simply rely on a general min function with multiple arguments.

See also: minimum, min, median of three, comparison operation.