Definition
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[1B1]By definition 1 “a set \( A \) is finite and has cardinality \(n\)” if it is equipotent to a set \(E_ n\) (for a choice of \(n ∈ ℕ\); note that there is at most one \(n\) for which this may hold, by the above Lemma). So when the set is finite, \(|A|\) is identified with the natural number of its elements; we will write \(|A|=n\). If a set isn’t finite, then it is infinite.