Cardinality of Empty Set
From ProofWiki
Theorem
- $\left|{S}\right| = 0 \iff S = \varnothing$
That is, the empty set is finite, and has a cardinality of zero.
Proof
Zero is defined as the cardinal of the empty set.
The result follows from Finite Cardinals and Ordinals are Equivalent.
Sources
- J.A. Green: Sets and Groups (1965)... (previous)... (next): $\S 1.3$
- T.S. Blyth: Set Theory and Abstract Algebra (1975): $\S 8$
