Point separating function I'm trying to prove that the set  $P = \{p: [0,1] \times [0,1] \to R \; \mid \; \text{p is a polynomial}\}$ is dense in $C( [0,1] \times [0,1], R)$. I'm stuck trying to find a points separating function. (obviously using the Stone Wierestrass approx).
Here is what I got so far: I thing the function that is the graph of $x$ and $\sin(x)$ should be points separating right?
Thanks!!

Another solution here would be to take 2 different functions: f(x,y) = x and g(x, y)= y
That works because it need not be one function that separates all points. 
