The main theorem is false: the paper's version of L'Hôpital's Rule is true in every ordered field, and the proofs of two key implications are circular or rely on an unstated stronger rule.
Principles of mathematical analysis
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L'H\^{o}pital's Rule is Equivalent to the Least Upper Bound Property
The main theorem is false: the paper's version of L'Hôpital's Rule is true in every ordered field, and the proofs of two key implications are circular or rely on an unstated stronger rule.