Question

Give a recursive definition for the set Y of all positive multiples of 9. That is, Y = {9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, ... }. Your definition should have a base case and a recursive part.

Answer 1

Recursion means defining something, such as a function, in terms of itself. So Y = {9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, ... }

Let f (0) = 0

So f ( n + 1) = f (n) + 9

f (1) = f(0) + 9 = 0 +9 = 9

f (2) = f(1) + 9 = 9 +9 = 18