There is at least 1 type of person in the world.

Given that there are n types of people, it is possible to construct an additional type of person by, say, naming them n+1 or something.

Thus, through induction, it is possible to prove that, while not necessarily infinite, the number of types of people are boundless. (There exists some type of person per natural number)

And yet, in this unlimited number of types of people, you manage to be the only one so uniquely you. :)