Is the universe discrete or continuous?

What proof is there that the universe is discrete and what proof is there that the universe is continuous?

You can never know if the universe is discrete for certain since even if it appears so there may still be some undetectable phenomena you are unaware of.

You can never find evidence to suggest the universe is continuous as there can never be a scientific instrument capable of infinite accuracy.

#34, yes, the "integers within the reals" is a model that fits the question, if that's how you need to frame the idea.  Even if our universe is discrete (i.e. like integers), it seems rational me that there is a continuous matrix that it still resides in (i.e. like the reals).

As for the model of electrons, it's true that they can inhabit certain places in atoms, but electrons fly off into "empty" space often enough.  Are you suggesting that as electrons traverse space, they only do so along discrete paths?  I've never heard of such a thing.  The discreteness of atomic orbitals only seems to apply to that particular situation -- electrons orbiting an atomic nucleus in close proximity with other electrons.