Math 360, Fall 2015, Assignment 1

The beginner...should not be discouraged if...he finds that he does not have the prerequisites for reading the prerequisites.

- P. Halmos

Carefully define the following terms, then give one example and one non-example of each:

1. Cartesian product (of two sets).
2. Relation (on a set $A$).
3. Relation (from $A$ to $B$).
4. Function (from $A$ to $B$).
5. Domain (of a function).
6. Codomain (of a function).
7. Image (of a function).
8. Injection (a.k.a. one-to-one function).
9. Surjection (a.k.a. onto function).
10. Bijection.
11. Equipotent (a.k.a. equinumerous or having the same cardinality).
12. Countable set.

Solve the following problems:

1. Section 0, problems 1, 5, 7, 11, 12, and 16.

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