Prove that f is injective.
What can you deduce about the relationship between the
cardinalities of N and N²?
(ii) Let p and q be integers. Prove that if 2^P = 3^q, then p = q = 0.
[Hint: consider separately all the possible cases of p and/or q being
positive/negative/zero.]
(iii) Let g: N² → N be the function given by g(m, n) = 2m3n.
Assuming the result from part (ii), or otherwise, prove that g is injective.
What can you deduce about the relationship between the cardinalities of N and N²?