## Abstract

Let (*a*_{ i })_{i∈I} be a family of cardinals indexed by a set *I*. The **cardinal sum** or simply the **sum** Σ_{i∈I} **a**_{ i } of (**a**_{ i })_{i∈I} is defined to be the cardinal of the union ∪_{i∈I}(**a**_{ix}). 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.

## Keywords

Real Number Natural Number Mathematical Logic Pairwise Disjoint Ordinal Number
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer Science+Business Media New York 1998