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Conceptual Mathematics, Second Edition by Stephen H. Schanuel, F. William Lawvere

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SESSION 2

Sets, maps and composition

1. Review of Article I

Before discussing some of the exercises in Article I, let’s have a quick review. A set is any collection of things. You know examples of infinite sets, like the set of all natural numbers, {0,1,2,3,…}, but we’ll take most of our examples from finite sets. Here is a typical internal diagram of a function, or map:

image

Other words that mean the same as function and map are transformation, operator, morphism, and functional; the idea is so important that it has been rediscovered and renamed in many different contexts.

As the internal diagram suggests, to have a map f of sets involves three things: ...

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