Ah, okay, so it boils down to the question whether real numbers are physically realizable.

There is a debate about that in the philosophy of physics and mathematics. AFAIK, according to the current state of physics real numbers cannot be realized within a finite amount of space, at least Gisin [1] recently argued that way and I've seen other arguments for this view before [2,3,4,5:167-170]. I also remember some argument based on thermodynamics but cannot find the reference.

[1] https://arxiv.org/pdf/1803.06824.pdf [2] https://arxiv.org/abs/math/0411418 [3] https://news.ycombinator.com/item?id=14080024 [4] https://ptolemy.berkeley.edu/~eal/pnerd/blog/are-real-number... [5] https://www.sciencedirect.com/science/article/pii/S030439750...