> 
> From [Algrebra by Gelfand](http://rads.stackoverflow.com/amzn/click/0817636773), it says that "When we claim that we have solved the equation $x^2-2=0$ and the answer is $x=\sqrt{2}$ or $x=-\sqrt{2}$, we are in fact cheating. To tell the truth, we have not solved this equation but confessed our inability to solve it; $\sqrt{2}$ means nothing except "the positive solution of the equation $x^2-2=0$
> 
> 
> 

Can someone please explain what he really means? Does he mean every irrational number is meaningless? Thanks in advance.