The set of squares of rational numbers is inductive.
How do we justify whether this statement is true of false?
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?
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?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?