Define a set S recursively as follows:

I. BASE: $1$ in S$,2$ in S$,3$ in S$,4$ in S$,5$ in S$,6$ in S$,7$ in S$,8$ in S$,9$ in S$.$

II$.$ RECURSION: If s in S and t in S$,$ then

a$)$ s$0$ in S

b$)$ st in S

III. RESTRICTION: Nothing is in S other than objects defined in I and II above