Corollary 1

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

Theory of Sets, chapter III, § 5. Properties of integers

The union E of a finite family $(\mathrm{X}_i)_{i \in \mathrm{I}}$ of finite sets is a finite set.

For the sum S of the family $(\mathrm{X}_i)$ is finite; and since there exists a mapping of S onto E (Chapter II, $\S\,4$ , no. 8), the set E is finite ( $\S\,4$ , no. 2, Proposition 2, Corollary 3).

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

alg-ii-s1-prop-23 not in this corpus
Exercise 1, § 4

Cites

Chapter II, § 4, no. 8
§ 4, no. 2, Proposition 2
Corollary 3