# Provide a recursive definition of the following sets

• March 2nd 2010, 11:41 AM
Runty
Provide a recursive definition of the following sets
I have some definitions that would apply to these, but I'm not sure whether or not they are very concrete, and I would also like to confirm that they are correct. Here are the sets and my current answers.

a) The set of odd positive numbers.
$1\in S$
If $x\in S$, then $x+2\in S$

b) The positive integer powers of 3.
$3\in S$
If $x\in S$, then $3\times x\in S$

c) The positive multiples of 4.
$4\in S$
If $x\in S, y\in S$, then $x+y\in S$

Are these all accurate, or would they benefit from more detailed answers?
• March 2nd 2010, 04:12 PM
MollyMillions
You've got the right idea, but it might be useful to use a bit different notation, since a recursion is asked for. Something like this for c) maybe:

Let $S$ be the set of positive multiples of 4.
$s_n \in S$
$s_0 = 4$
$s_n = s_{n-1} + 4$