Proposition 3

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

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

Let X and Y be sets. If there exists a surjection $f$ of X onto Y, then Card (Y) $\leqslant$ Card (X).

For there exists a section $s$ associated with $f$ (Chapter II, § 3, no. 8, Proposition 8) and $s$ is an injection of Y into X.

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

Corollary 3, § 4
Proposition 4, § 6
top-i-s1-prop-6 not in this corpus

Cites

Chapter II, § 3, no. 8, Proposition 8