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?
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?
As you have presented the question, it is not true.
Consider: $\displaystyle \mathcal{S} = \mathbb{Z}^ + \cup \left\{ {n + 0.5:n \in \mathbb{Z}^ + } \right\}$.
Clearly $\displaystyle \mathcal{S}$ has both properties required, contains 1 and is closed with respect to addition.
But $\displaystyle \mathcal{S} \ne \mathbb{Z}^ +$.
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?