### Define: Functions

Let A and B be nonempty sets. A **function f ** from A to B, which is denoted f: A –> B, is a relation from A to B such that all a ∈ Dom(f), f(a), the f-relative set of a, contains just one element of B. Naturally, if a is not in Dom(f), then f(a) = ∅. If f(a) = {b}, it is traditional to identify the set {b} with the element b and write f(a) = b.

### Simplified Definition: Functions

Definition 1.a: ...

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2012