max2

Max2 is a term used in mathematics and computer science to denote the binary maximum operation: a function that takes two inputs and returns the greater of the two. It is often contrasted with the general notion of a maximum over a set or with n-ary versions that accept more than two arguments. In formal contexts, max2 serves as a precise two-argument primitive from which larger maximums can be built by chaining calls.

In programming and numerical computing, max2 is typically implemented as a simple comparison: given inputs a and b, the function returns a if a is greater than or equal to b, otherwise it returns b. The operation is commutative and idempotent (max2(a, a) = a). When extended to sequences, many languages provide a generic max function that effectively acts as max2 when applied pairwise and iteratively to combine multiple values. In floating point arithmetic, behavior with non-finite values such as NaN depends on the language or library; some implementations propagate NaN, while others return the finite input or a defined result.

Examples illustrate its use: max2(3, 7) equals 7, and max2(-4, -9) equals -4. In floating point contexts, max2(1.0, NaN) may yield 1.0 or NaN depending on the environment.

Max2 is not universally a standard named function across languages; many systems simply provide a two-argument max function (often named max) without the explicit label max2. The term is common in explanations and textbook material as a precise, two-argument building block for broader optimization, sorting, and decision procedures.