Logically thinking it should be discrete, otherwise movement of a point in space would be impossible since the point would be stuck in an infinite endless loop, as stated by Zeno's paradox. And yes, there is a mathematical solution to that, but in that solution we are ignoring the factor of time, wouldn't time go on endlessly before it can even move? I honestly can't wrap my head around this. Aren't we missing a major piece somewhere cutting the link between what we think, the math and reality?