# Math Help - Prove or Disprove

1. ## Prove or Disprove

The set of squares of rational numbers is inductive.

How do we justify whether this statement is true of false?

2. Originally Posted by harish21
The set of squares of rational numbers is inductive.

How do we justify whether this statement is true of false?
Inductive set in what way? I define inductive set as being a partially ordered set that fulfills the criteria to apply Zorn's lemma. How do you define it?

3. Originally Posted by Drexel28
Inductive set in what way? I define inductive set as being a partially ordered set that fulfills the criteria to apply Zorn's lemma. How do you define it?
The book has given no definition. The only thing it states about a set being inductive is that (i) the number 1 should be in S and (ii) if x is in S, then x+1 is also in S. There was a similar question that had asked to prove or disprove that the set of irrational numbers is inductive. That statement was false because 1 is not an irrational number, and this would violate the rule for the set to be inductive.
I think the question I have posted is also to be done in a similar way, but I cannot think how we are supposed to do it! any idea?

4. Originally Posted by harish21
The book has given no definition. The only thing it states about a set being inductive is that (i) the number 1 should be in S and (ii) if x is in S, then x+1 is also in S. There was a similar question that had asked to prove or disprove that the set of irrational numbers is inductive. That statement was false because 1 is not an irrational number, and this would violate the rule for the set to be inductive.
I think the question I have posted is also to be done in a similar way, but I cannot think how we are supposed to do it! any idea?
Uh...if that is all you need to prove. Note that $1\in\mathbb{Q}$ and $\frac{p}{q}+1=\frac{p+q}{q}$...

5. Originally Posted by harish21
The book has given no definition. The only thing it states about a set being inductive is that (i) the number 1 should be in S and (ii) if x is in S, then x+1 is also in S.
That is a definition!

There was a similar question that had asked to prove or disprove that the set of irrational numbers is inductive. That statement was false because 1 is not an irrational number, and this would violate the rule for the set to be inductive.
I think the question I have posted is also to be done in a similar way, but I cannot think how we are supposed to do it! any idea?
Is 1 a square number? If not you are done. If it is, then look at 1+ 1= 2. Is 2 a square number?

6. Originally Posted by Drexel28
Uh...if that is all you need to prove. Note that $1\in\mathbb{Q}$ and $\frac{p}{q}+1=\frac{p+q}{q}$...
Originally Posted by HallsofIvy
That is a definition!

Is 1 a square number? If not you are done. If it is, then look at 1+ 1= 2. Is 2 a square number?