Let (a i )i∈I be a family of cardinals indexed by a set I. The cardinal sum or simply the sum Σi∈I a i of (a i )i∈I is defined to be the cardinal of the union ∪i∈I(aix). If a and b are cardinals then the sum a+ b of a and b is defined to be the cardinal of (a × 0) ∪ (b × 1). Notice that in these definitions the sets forming the unions are equipotent to the cardinals being added but (thanks to their second factors) are pairwise disjoint.
KeywordsReal Number Natural Number Mathematical Logic Pairwise Disjoint Ordinal Number
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