MATH.17:9 - Consequences

Operations become available for construction, comparison and change. A law established for the higher-order construction can replace repeated case-by-case reasoning, while a counterexample can identify a proposed change that needs revision.

The abstraction has a cost: the operation collection and its laws must be constructed. It pays when the rule itself is changing or when one result will organize many operations. Questions about implementation, approximation or real interaction can require further structure beyond the function account.