Next we looked at the problem of checking a sorting program. It is not enough to verify that the numbers are in non-decreasing order; we must also check that the input and output are the same as multisets. After a false start following a student's suggestions we did this by evaluating the polynomials P(x)=(x-a1)(x-a2)...(x-aN) and Q(x)=(x-b1)(x-b2)...(x-bN) at random points from a large set, where {a1,...,aN} and {b1,...,bN} are the multisets we are trying to test for equality. We used the "fundamental theorem of algebra" to see that this worked.