Q:

Question about the existence of points and lines.

Say we draw a point on a graph. If the point should not take up any area than how come we could see it. Say we graph $y=x^2$, we obviously could see it. However, because $y=x^2$ is a function made up of a collection of points with no area, how come we see it? How come we see lines if they have no area?

A:

We don't draw a point, we draw a representation of a point.  If we drew a point, we couldn't see it. The ideal graph of $y = x^2$ would also be invisible, which wouldn't give us a whole lot of information. The representation of the graph is not the graph, because we can see it, it is inaccurate; but it does give us more information than the real graph would.

