Math 360, Fall 2018, Assignment 2

No doubt many people feel that the inclusion of mathematics among the arts is unwarranted. The strongest objection is that mathematics has no emotional import. Of course this argument discounts the feelings of dislike and revulsion that mathematics induces....

- Morris Kline, Mathematics in Western Culture

Read:

1. Section 0.

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

1. Subset (of a given set).
2. Improper subset (note that we did not discuss this in class, so you may need to look in the book for the definition).
3. Empty set.
4. Cartesian product (of two sets).
5. Binary relation (on a set $A$).
6. Reflexive (binary relation).
7. Symmetric (binary relation).
8. Transitive (binary relation).
9. Equivalence relation.
10. Equivalence class (of an element $a\in A$, with respect to an equivalence relation $\sim$ on $A$; also known as $\left[a\right]_\sim$).

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

1. Russell's paradox (this is not really a theorem, but it is an important fact).
2. Theorem concerning the relationship among equivalence classes for a given equivalence relation.

Solve the following problems:

1. Section 0, problems 1, 2, 3, 4, 5, 6, 7, 8, 11, 16, 29, 30, 31, 32, and 36.

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