(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The set of squares of rational numbers is inductive

2. Relevant equations

definition of an inductive set

3. The attempt at a solution

sorry i know this is probably very easy to most but I am just learning analysis. Okay, so we can see that 1 is in the set because it is rational and 1^{2}exists. Am I correct in thinking that it doesn't matter whether or not 1^{2}is rational? I mean obviously it is, but aren't we really just checking to make sure that S(1) is defined? Then for the second part, we can take S(x) to be x^{2}whenever x=m/n, where m,n are integers and either m or n is odd. Again, aren't we basically proving that if S(x) exists, or (m^{2}/n^{2}) exists, then S(x+1), or [(m+n)^{2}/n^{2}] also exists. But then don't I also need to show that if x is rational, then so is x+1? Maybe i am reading way too much into this, but again I am new to these and I'm trying to understand exactly what I need to show.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: The set of squares of rational numbers is inductive

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