# Thread: Show that the set S defined by 1 Element S... HELP!

1. ## Show that the set S defined by 1 Element S... HELP!

Show that the set S defined by 1 Element S and s + t Elemeent S whenever s Element S and t Element S is the set of positive integers.

I do not know how to even start this problem. I know you use induction right? Any other hints?

2. Originally Posted by mathsucks99
Show that the set S defined by 1 Element S and s + t Elemeent S whenever s Element S and t Element S is the set of positive integers.
As you have presented the question, it is not true.
Consider: $\mathcal{S} = \mathbb{Z}^ + \cup \left\{ {n + 0.5:n \in \mathbb{Z}^ + } \right\}$.
Clearly $\mathcal{S}$ has both properties required, contains 1 and is closed with respect to addition.
But $\mathcal{S} \ne \mathbb{Z}^ +$.

3. i dont quite get what your saying. your saying the problem i wrote cannot be true? I use Element for the (element sign) cause i cant type it in...

Your saying the whole set S cannot be the set of positive integers?

4. Originally Posted by mathsucks99
i dont quite get what your saying. your saying the problem i wrote cannot be true?
As I have shown the way that you have written the problem it is false.
I suspect that you want $\mathcal{S} \subseteq \mathbb{Z}^ +$.
In which case the statement is true.
But if you don’t know the difference, how can we possibly help you?

5. Ok but this is the problem from the homework verbatim:

Show that the set S defined by 1 ∈ S and s + t ∈ S whenever s ∈ S and t ∈ S is the set of positive integers.

So i cannot do this answer and should write that down your saying? i dont quite get it obviously.

Do i use structural induction, recursion?