Remark

Tag 08H8, permanent. Cite it as [Bourbaki, Tag 08H8].

Functions of a Real Variable, chapter V, Appendix 0. Hardy Fields. (H) Functions

Note that two equivalent (H) functions can have non-equivalent inverses, as the example of the two functions $\log x$ and $1 + \log x$ shows.

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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