Example 3

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

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

We have seen that $\sin^2 x \preccurlyeq \sin x$ as $x$ tends to $+\infty$ , but we do not have $\sin^2 x \simeq \sin x$ , even though these functions vanish at the same points.

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

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