Math 2200 Homework 4
Due Date: February 20
This week’s homework assignment is light, so catch your breath and spend some time going back over the
material on sets and functions. Make sure you understand everything in Chapter 3! I have recently posted
three documents giving complete proofs for all the important exercises in Chapter 3 and for the problems
on Learning Celebration #2. Practice solving those exercises, and then compare your answers with the
solutions. You cannot escape sets and functions if you want to continue studying mathematics, so any time
you invest now will be worthwhile!
If you’re confused by any of the material in Chapter 3, e-mail me with questions or to set up a meeting, or
just stop by my office. There is no shame in struggling with the material or proof techniques – mathematics
is really difficult, and confusion is a good sign because it shows you are grappling with the concepts we are
learning. The bane of a mathematician is thinking you understand something when you really don’t.
Submit your solutions in class on Wednesday or by 5 PM in my office.
Exercises to be Submitted
3.5.13
Not to be Submitted
Challenge problem: Prove or disprove the following claim.
Claim. Let A and B be sets. Suppose there is an injective function A
g
! A . Then there is a bijective function A h ! B .
B
(Hint: First consider the case when A and B are finite.)
1
f
! B and an injective function