Suppose f:R->R is continuous and f(r)=$\displaystyle r^2$ for each rational number r. Determine f($\displaystyle \sqrt{2}$) and justify your conclusions.
I have no clue
so wait does that just mean it would be 2? And would we have to show it by showing that the limit of lim_r->$\displaystyle \sqrt{2}$ f(r)=2 which is equal to f($\displaystyle \sqrt{2}$)..Or can we say that since it is continuous we know that lim as r->$\displaystyle \sqrt{2}$ of f(r)=f($\displaystyle \sqrt{2}$)? which is why we know its 2? I hope its not getting confusing.