# Thread: Proof for every Natural number

1. ## Proof for every Natural number

Hi, I'm needing some help with an exercise

Let A be {k^2|k belongs to N}. I need to if A holds the following proposition: "For every n that belongs to N, if n belongs to A then n+1 belongs to A."
My problem is on the way the set is defined, as far as I understand it, A should be {1,4,9,16,25,36...}.

I will appreciate any response as long as it doesn't reveal the solution to the problem... tnx in advance...

2. ## Re: Proof for every Natural number

Originally Posted by jfk
Let A be {k^2|k belongs to N}. I need to if A holds the following proposition: "For every n that belongs to N, if n belongs to A then n+1 belongs to A."
My problem is on the way the set is defined, as far as I understand it, A should be {1,4,9,16,25,36...}.
If I were you, I would double check the exact wording of this question.
As stated, it is false.

3. ## Re: Proof for every Natural number

I'm sorry. I just saw what wrote before (lol).
What I meant:
"Let A be {k^2|k belongs to N}. I need to state if A holds or not the following proposition: "For every n that belongs to N, if n belongs to A then n+1 belongs to A."

By the way A should be {1,4,9,16,25,36...}? is that correct?

4. ## Re: Proof for every Natural number

Originally Posted by jfk
I'm sorry. I just saw what wrote before (lol).
What I meant:
"Let A be {k^2|k belongs to N}. I need to state if A holds or not the following proposition: "For every n that belongs to N, if n belongs to A then n+1 belongs to A." By the way A should be {1,4,9,16,25,36...}? is that correct?
$\displaystyle 4\in A$ BUT $\displaystyle 4+1\notin A$. SO?

5. ## Re: Proof for every Natural number

your A is correct (assuming you are working with $\displaystyle N_1$ and not $\displaystyle N_0$).

As written your problem seems very easy (the proposition is false and there is no shortage of counter examples), as plato said...are you sure you have written the question down properly

edit: didn't see platos post :P

6. ## Re: Proof for every Natural number

Thank you all for the responses, now I understand. By the way... if "A" would be the "Empty Set" then the claim will hold since it's a vacuous truth rigth?

7. ## Re: Proof for every Natural number

Yes, but your A here is NOT empty so I don't understand why you are asking this.