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.

Discussing (or in fact even thinking about) statements with unknowable truth-values is a waste of time. Pretty much by definition, the answer to the 'what if' question is always going to be 'it wouldn't affect anything'.