EDB — 22B

[22B]For convenience we will use the symbol \(|A|\) to indicate cardinality of the set \(A\). This symbol is used as follows. Given two sets \(A,B\), we will write \(|A|= |B|\) if these sets are equipotents (or sometimes equinumerous), i.e. if there is a bijective function between \(A\) and \(B\); we will write \(|A|≤ |B|\) if there is an injective function from \(A\) to \(B\). We will also write \(|A|{\lt} |B|\) if there is an injective function from \(A\) to \(B\), but not a bijection. If we assume the axiom of choice to be true, then for every pair of sets we always have \(|A|≤ |B|\) or \(|B|≤ |A|\) (see [03F]↺↻).