Corollary

Tag 03R2, permanent. Cite it as [Bourbaki, Tag 03R2].

Theory of Sets, chapter III, § 3. Equipotent sets. Cardinals

Let $\mathfrak{a}$ , $\mathfrak{b}$ , $\mathfrak{c}$ be cardinals. Then

(1)

\mathfrak{a} + \mathfrak{b} = \mathfrak{b} + \mathfrak{a}, \qquad \mathfrak{a}\mathfrak{b} = \mathfrak{b}\mathfrak{a};

(2)

\mathfrak{a} + (\mathfrak{b} + \mathfrak{c}) = (\mathfrak{a} + \mathfrak{b}) + \mathfrak{c}, \qquad \mathfrak{a}(\mathfrak{b}\mathfrak{c}) = (\mathfrak{a}\mathfrak{b})\mathfrak{c};

(3)

\mathfrak{a}(\mathfrak{b} + \mathfrak{c}) = \mathfrak{a}\mathfrak{b} + \mathfrak{a}\mathfrak{c}.

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-i-s1-n3-exa-1 not in this corpus
alg-i-s1-n5-exa-1 not in this corpus
alg-i-s2-lem-2 not in this corpus
Proposition 1, § 5

Cites

Nothing.