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!!

I'm sorry I misunderstood your notation initially. 
$x \mapsto \sin(x)$ isn't a polynomial function, so we'll have to try something else. 
Here's something. Pick a point $(x_0,y_0) \in [0,1]^2$. Then the square of the distance between $(x_0,y_0)$ and another point $(x,y)$ is a familiar polynomial in $x$ and $y$, and is only $0$ if $(x,y) = (x_0,y_0)$.
Note that this is actually way more than we need; this function works for our initial point $(x_0,y_0)$ and any other point.
