ROBERT E. GOMPF
Department of Mathematics
The University of Texas at Austin
Austin, TX 78712-1082
University of California at Berkeley
Robion C. Kirby
M365C Homework #1 Solutions
II #2a. We must show that ba is the additive inverse of ab, i.e., (ab)+(ba) = 0.
But the left side is (by denition) a + (b) + b + (a). The order of addition doesnt
matter by associativity, so by the denition of additive inverse
C. H. Colbert
1 Prove that if X and Y are countable sets, then X Y is a countable set.
1S Proof. Let X and Y be countable sets and assume there are bijections f : X N and g :
Y N. Dene a set map : X Y N N as (x, y) = (f (x), g(y). We claim t