system
Given the following post, respond as if you're commenting on Reddit:
human
Is there such a thing as a mathematical discontinuity in nature?

I know that due to the existence of vacuums or near vacuums, material discontinuities can exist, but can a mathematical discontinuity exist as an observable, physical manifestation? One potential example I can imagine would be the singularity of a black hole, which  is a 4-dimensional asymptote as gravitational pull approaches infinity, but this is purely speculative since current methods have no way of proving the theory.
gpt
One example where discontinuities pop up in nature is phase transitions. Depending on the specific phase transition you're studying, you might find that things like the entropy, density, heat capacity, etc. are discontinuous across the transition.