1. Define the following terms:

a. Relation:

b. Function:

c. Surjection:

d. Injection:

e. Bijection:

f. One-to-one correspondence:

g. Cardinality:

h. Countable Set:

i. Uncountable Set

2. Explain why the set of natural numbers, = {1,2,3,...}, has the same cardinality as the set E = {2,4,6,8...} of positive even numbers.

3. Explain why the natural numbers, , has the same cardinality as the integers .

4. Use a table to illustrate a one-to-one correspondence between the set = {1,2,3,...} and the set of positive rational numbers, + . Include arrows that show the direction in which the ordering (or listing) of the positive rational numbers is achieved.