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?