english - What is the smallest set of letters that can spell any integer?

Today my 9-year-old nephew told me that he can spell any integer in English using only 9 letters. This is how he's doing it:

    ...
-3: MINUS ONE MINUS ONE MINUS ONE
-2: MINUS ONE MINUS ONE
-1: MINUS ONE
 0: ONE MINUS ONE

 1: ONE
 2: ONE PLUS ONE
 3: ONE PLUS ONE PLUS ONE
    ...

The letters he's using are E, I, L, M, N, O, P, S and U.

Can we do better and spell any integer with less than nine letters? I think so!

Just please be sure to briefly explain any maths you are using in your method, so that my young nephew (and his uncle) can understand.