Maps and relations

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Chapter 2 Maps and relations

We relate different sets by means of maps. The notion of a map is critical for a complete understanding of sets and their relationship to numbers — i.e., counting.

Maps can be injective, surjective, both, or neither. Roughly speaking, these adjectives describe how information is transmitted through a map. Counting is really about the construction of bijections.

Finally, relations on a set provide a useful way to compare elements of that set. These play a critical role in the study of algebraic structures and orderings, which are the topic of the next chapter.