Bourbaki

Example 2

Tag 03T6, permanent. Cite it as [Bourbaki, Tag 03T6].

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

All sets consisting of a single element are equipotent, since {(a,b)}\{(a, b)\} is the graph of a bijection of {a}\{a\} onto {b}\{b\}; in particular, they are all equipotent to {∅}\{\emptyset\}. The cardinal Card({∅})=τZ(Eq({∅},Z))\mathrm{Card}(\{\emptyset\}) = \tau_Z(\mathrm{Eq}(\{\emptyset\}, Z)) is denoted by 1. [^1]

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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Cites

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Transcribed from the printed edition, 2004, Springer. Not translated.