Single symbol alphabet is more interesting, (empty string = 0, sucessor function = append another symbol) the system you describe is more succinctly described using a concatenation operator:

• 0 = 0, 1 = S0, 2 = S1 ... 9 = S8.
• For All b in {0,1,2,3,4,5,6,7,8,9}, a in N: ab = a x S9 + b

From these definitions we get, example-wise:

• 10 = 1 x S9 + 0 = SSSSSSSSSS0