[CuriouslyC]

General relativity and the standard model also produce infinite values, which to me is a pretty sure sign your model is broken. Viewing black holes as infinitely dense hasn't yet caused us problems in terms of predictions (but they're still a bit wild west area), and they fixed the standard model with renormalization (which seems like a bit of a hack). They're good enough to be useful but I'm pretty sure everyone expects them to be radically reformulated at some point.