1. determine f(sqrt(2))?

Suppose f:R->R is continuous and f(r)= $r^2$ for each rational number r. Determine f( $\sqrt{2}$) and justify your conclusions.

I have no clue

2. Originally Posted by tn11631
Suppose f:R->R is continuous and f(r)= $r^2$ for each rational number r. Determine f( $\sqrt{2}$) and justify your conclusions
If $f:\mathbb{R}\to\mathbb{R}$ is continuous then if $(x_n)\to x_0$ then it is the case that $f\left(x_n\right)\to f\left(x_0\right) .$

3. Originally Posted by Plato
If $f:\mathbb{R}\to\mathbb{R}$ is continuous then if $(x_n)\to x_0$ then it is the case that $f\left(x_n\right)\to f\left(x_0\right) .$
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-> $\sqrt{2}$ f(r)=2 which is equal to f( $\sqrt{2}$)..Or can we say that since it is continuous we know that lim as r-> $\sqrt{2}$ of f(r)=f( $\sqrt{2}$)? which is why we know its 2? I hope its not getting confusing.