Thread: 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...

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.

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?

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?

BUT . SO?

your A is correct (assuming you are working with and not ).

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

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?

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