Math 360, Fall 2013, Assignment 2

By one of those caprices of the mind, which we are perhaps most subject to in early youth, I at once gave up my former occupations; set down natural history and all its progeny as a deformed and abortive creation; and entertained the greatest disdain for a would-be science, which could never even step within the threshold of real knowledge. In this mood of mind I betook myself to the mathematics, and the branches of study appertaining to that science, as being built upon secure foundations, and so worthy of my consideration.

- Mary Shelley, Frankenstein

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

1. Function (from a set \(A\) to a set \(B\)).
2. Injection.
3. Surjection.
4. Bijection.
5. Same cardinality.
6. Root of unity.
7. Binary operation.
8. Closed (under a given binary operation).
9. Associative.
10. Commutative.
11. Composition (of two functions).

Carefully state the following theorems (you need not prove them):

1. Theorem relating equivalence relations to partitions.
2. Associativity of composition.

Solve the following problems:

1. Section 0, problems 12 and 16.
2. Section 1, problems 3 and 13.
3. Section 2, problems 2, 3, 7, 10, and 11.

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Questions:

1) I still don't get what non - example means for math. Can someone please explain?? Thank you!!