Cardinal product
= Cardinal product
{title2=$\prod_{i\in I}\kappa_i$}
The cardinal product is the <cardinality> of the set of functions $f$ on the index set with $f(i)<\kappa_i$ at every coordinate. The empty product is one, because it contains the <empty function>. A zero factor makes a nonempty-index product zero. In ZFC, a family of nonzero cardinals has nonzero product by the <axiom of choice>.