[tsimionescu]

Current physical models don't have the universe itself (space-time) quantized - only matter is quantized. Even the planck time and planck length only represent minimal measurable distances/durations - the maths still assume that two things can be separated by fractional multiples of these.

That's not to say that physics requires infinities, but current models also don't disallow infinity.

Of course, actual infinity is outside the purview of science - there is no way to differentiate between infinity and something too big/small to measure, even in principle. Apparent paradoxes related to infinity, such as Banach-Tarski, don't change this, as they also require infinite precision to realize, making them impossible to test as well - even if a sphere is indeed made up of an infinity of space-time points, and even if we could manipulate those, we wouldn't be able, in finite time, to extract the necessary infinite subsets of points to create the two spheres from one.

[rob_c]

Physics doesn't require infinities, but it's scary how well QED/QFT approximates the g-factor (https://en.m.wikipedia.org/wiki/G-factor_(physics) ) for electrons given the amount of renormalization (cancelling of infinities) needed to estimate the true value in nature.