# Is every (possibly infinite) sum of cardinal numbers defined?

Hrbacek and Jech gives the following definition of cardinal addition:

My question is: given an indexed system of cardinals $$\left \langle \kappa_{i} |i\in I \right \rangle$$ does there exist a system $$\left \langle A_{i} |i\in I \right \rangle$$ of mutually disjoint sets such that $$|A_{i}|=\kappa_{i}$$ for all $$i \in I$$?

Yes. Just let $$A_i=\{i\}\times \kappa_i$$, for instance.