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Also, a circle is an infinite set of points, so even if points were visible, you couldn't have a real circle without infinite points.

By that definition, nothing is visible. You never see anything except photons.

That's true; and sometimes, that definition is useful, as it is here.

Visible means "able to be seen." You can see things that emit or reflect light. Abstract concepts don't emit or reflect light.

Real objects can only approximate a circle. The pedantic definition of a circle in this context is being used to make the point that you can't make a perfect circle with pixels.

No. If you made an abstract object that emitted light, like the "linear light source" I hypothesized, it would be a perfect circle, and visible. It doesn't exist, of course, but if it did, it would be visible... ;-)

Richard Feynman spoke well and humorously on this topic: http://http://www.youtube.com/watch?v=XpYhM4x4PmY