set cardinality

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• review cardinality
• set cardinality: number of elements in a set, either finite or infinite
• Two sets $A$ and $B$ have the same cardinality (written as $|A|=|B|$) IFF there exists a bijection $f:A\to B$
• Set $A$ has cardinality $\ge$ set $B$ (written as $|A|\ge |B|$ ) IFF there exists
  • an injection $g:A\to B$
  • a surjection $g^{\prime }:B\to A$