Remark 1

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

Functions of a Real Variable, chapter V, § 1. COMPARISON OF FUNCTIONS ON A FILTERED SET

Two functions in $\mathscr{H}(\mathfrak{F}, \mathbf{R})$ need not be weakly comparable, as is shown by the example of the functions 1 and $x \sin x$ as $x$ tends to $+\infty$ .

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

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