Bonus Problem #1

10 points

When writing your solution to this problem, you should address the following points:

• Write legibly so your work is easily graded,
• Write in complete sentences,
• Use examples in all parts of the problem to support your conclusions, and
• Use correct, applicable mathematical vocabulary in your responses.

Consider the set of odd, whole numbers:

O = {1, 3, 5, 7, 9, 11, 13,…}

1. Is set O closed under addition? Why or why not?
2. Is set O closed under multiplication? Why or why not?
3. Does set O have an additive identity? Why or why not?
4. Does set O have a multiplicative identity? Why or why not?
5. Is it possible to set up a 1 – 1 correspondence between set O and the counting numbers? Why or why not?

The problem solution and answers are due at the beginning of the hour on Thursday, March 1.