Proposition 2

Tag 03N8, permanent. Cite it as [Bourbaki, Tag 03N8].

Theory of Sets, chapter III, § 6. Infinite sets

Every countable infinite set E is equipotent to $\mathbf{N}$ .

For $\mathrm{Card}(\mathrm{E}) \leqslant \mathrm{Card}(\mathbf{N})$ by definition; and $\mathrm{Card}(\mathbf{N}) \leqslant \mathrm{Card}(\mathrm{E})$ since E is infinite.

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

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