Outside of some tricks with language ("this statement is a lie"), you can't have actual paradoxes. By definition, a real paradox is impossible. However, you can get things that seem paradoxical. Normally, these situations involve reasoning that seems good, based on common assumptions, that leads to a result that contradicts what we know to be true.

So, we know that a racer can overtake another racer that has a headstart on him. Zeno's reasoning seems solid, but indicates that overtaking should be impossible. The common assumption that turns out to be wrong is the idea that space is infinitely divisible. We're in a simulation, and you can't have half-a-pixel, so you have to always move across the screen in discrete units.