It is an unresolved question whether the universe is discrete or continuous in its intricate quantum level structure.
It is often stated that it is beyond our reach to resolve this issue. See for example: Is time continuous or discrete?
Is this however really true? Consider a simple dynamical system, such as the Lorenz attractor. When you solve this system numerically it quickly becomes evident that the solutions found depend heavily on the numerical precision. The number of revolutions around one attractor point before the evolving curve moves to the other attractor point varies with numerical precision. At some point you can wonder if you are really studying general behavior rather than a near exact solution.
Would it be possible to set up an actual experiment with a highly non-linear system, exhibiting long term iteration, to show whether or not the real-world solution at some point deviates from high-precision numerical simulation?