The moment infinity ends, every paradox probably resolves itself.
A being we'll call Ent for simplicity's sake. Ent is a being that has possession over the quantum field and all it's effects, and is omnipotent. Because Ent has possession over the quantum field, he can see the probability of what outcomes will happen, and since he's omnipotent, he can alter those outcomes or remove them entirely, and he decides to remove infinity from every outcome in which it exists. Now what? First off, paradoxes that rely on infinity break, so do circles, and basically anything that goes in a loop for eternity, AKA an endless loop, AKA an infinite loop, something like the Penrose staircase or mobius strip. Let's go over the paradoxes: Thompson's lamp paradox is when you turn a lamp on and off at an infinite speed forever, thus, a paradox that relies on infinity, which is a rule that have been broken. The Achilles and the tortoise paradox is when a racer reaches halfway towards a tortoise, but the tortoise has moved on, and Achilles does the same thing again, but so does the tortoise for an infinite amount of time forever, thus, a paradox that relies on infinity. There're a lot more paradoxes that rely on infinity to exist, but we'll leave the paradoxes alone now and move onto pi, the circumference of a circle. Pi goes on forever, it has infinite digits, simple as that. But now it's not simple as that, because infinity is gone, so how many digits does pi have now? Btw my name's Alex, and I hope I broke your brain as hard as physically possible. Have a good day and a good time trying to fix your brain.