MATH.17:4.1 - Specify the operations and the question about them

Name the inputs and outputs of an operation. Write f:A -> B when f assigns an element of B to every element of A. Write g∘f for “first f, then g”; it is defined when f’s output is an allowed input to g.

Choose what counts as equality for the present question. In the main function route, f and g are equal when they have the same domain and codomain and f(x)=g(x) for every input x. If the question concerns the steps used, resource cost or another distinction between ways of producing that function, retain a construction or program representation carrying that distinction. A function value alone leaves it unavailable. MATH.1 supplies constructions retaining ordered steps; MATH.2 handles an identification when the needed operations respect it.

Formulate the intended operation on rules. It might take two operations and compose them, send an operation on individual inputs to an operation on collections, or turn an expression for a function into another expression. State which result matters: admissibility, an identity, a comparison, a changed construction, or a failed requirement.