Concept · Foundations

Function

A function f: A → B is a relation from A to B such that for every a ∈ A there is exactly one b ∈ B with (a, b) ∈ f; we write f(a) = b for this unique value.

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Why it matters

Functions capture the idea of well-defined assignment and are the most widely used relational structure in mathematics and logic.

Where this shows up

Units and lessons using this concept

Following the links will take you to the page where this term is introduced in context.

Units (1)

Set Theory and Relations: The Structure Underneath LogicStudents learn the language of sets, relations, and functions that underlies most of modern formal logic. They master set operations, rel…

Lessons (2)

Capstone: Using Set Theory in Logic and ArgumentSet Theory and Relations: The Structure Underneath Logic Functions and CardinalitySet Theory and Relations: The Structure Underneath Logic

Other concepts in Foundations

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