First, by the previous theorem, the Minority Groups are infinite in number. Let M be the set of minority groups and define a function f: N -> M by f(n)=The nth alphabetical minority group. The alphabetization method being used here places symbols and names at the end. We show that f is bijective.

Injective: In the previous theorem, our definition implied that a minority group must have a different name than all other minority groups in order to count. Therefore there will be no “ties” in alphabetical order, i.e. cases in which f(x)=f(y) but x=/=y for some x, y in N. Therefore f(n) is injective.

Surjective: We want to show that for all m in M there exists n in N such that f(n)=m. Simply choose n such that m is the nth alphabetically listed minority group. Thus, f is surjective.

We have shown that f is injective and surjective, and so it is bijective. Since there exists a bijective function between natural numbers and minority groups, the minority groups are dennumerable as well as destitute and discriminated against.