L'H\^{o}pital's Rule is Equivalent to the Least Upper Bound Property
Classical Analysis and ODEs
2025-05-30 v1
Abstract
We prove that, in an arbitrary ordered field, L'H\^{o}pital's Rule is true if and only if the Least Upper Bound Property is true. We do the same for Taylor's Theorem with Peano Remainder, and for one other property sometimes given as a corollary of L'H\^{o}pital's Rule.
Cite
@article{arxiv.2505.23092,
title = {L'H\^{o}pital's Rule is Equivalent to the Least Upper Bound Property},
author = {Martin Grant and Kyle Hambrook and Alex Rusterholtz},
journal= {arXiv preprint arXiv:2505.23092},
year = {2025}
}