While I understand that the use of the term 'mathematical limit' is meant to imply a stable equilibrium, in this context it does make it sound as if there are rigorous mathematical proofs that these unmentioned things are indeed inevitable. I'm not sure if that's what you meant to convey.
I think a better choice of word might have been "asymptote". Thanks for pointing this out.
At the risk of being a bit pedantic, limits don't imply stability, though, only that something is heading in a certain direction, and may or may not be reached.
