Proposition 3

Tag 03N9, permanent. Cite it as [Bourbaki, Tag 03N9].

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

Every infinite set has a partition $(\mathrm{X}_\iota)_{\iota \in \mathrm{I}}$ formed of countable infinite sets $\mathrm{X}_\iota$ , the index set I being equipotent to E.

For $\mathrm{Card}(\mathrm{E}) = \mathrm{Card}(\mathrm{E})\ \mathrm{Card}(\mathbf{N})$ (no. 3, Theorem 2, Corollary 4).

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.

Cited by

Exercise 3, § 6
Exercise 5, § 6

Cites

no. 3, Theorem 2
Corollary 4