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**tttcomrader** Suppose that the function $\displaystyle f: \mathbb {R} ^n \rightarrow \mathbb {R} $ is continuous and that $\displaystyle f(u)>0$ if the point $\displaystyle u \in \mathbb {R} ^n $ has at least one reational component. Prove that $\displaystyle f(u) \geq 0 $ for all points [tex] u \in \mathbb {R} ^n

Proof so far:

Suppose that $\displaystyle u = (u_1,u_2,...,u_k,...,u_n) $ with $\displaystyle u_k \in \mathbb {Q} $, so that $\displaystyle f(u)>0 $

I want to show that $\displaystyle f(v) \geq 0 \ \ \ \ \ \forall v$