Examples

Tag 0E5I, permanent. Cite it as [Bourbaki, Tag 0E5I].

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

1) The relation $f \preccurlyeq 1$ means that $f$ is bounded on a set of $\mathfrak{F}$ .

2) For every function $f$ of $\mathscr{H}(\mathfrak{F}, V)$ , and every scalar $\lambda \neq 0$ , one has $f \preccurlyeq f \lambda$ . 3) When $x$ tends to $+\infty$ one has $\sin^2 x \preccurlyeq \sin x$ . 4) When $(x, y)$ tends to $(0, 0)$ in $\mathbf{R}^2$ one has

xy \preccurlyeq x^2 + y^2.

The following propositions are immediate consequences of def. 1:

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

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