The usual choice is for '' I '' to be infinite and '' U '' to contain all cofinite subsets of '' I '' , otherwise the ultrafilter is principal , and the ultraproduct is isomorphic to one of the factors .
The usual choice is for '' I '' to be infinite and '' U '' to contain all cofinite subsets of '' I '' . 
 Otherwise the ultrafilter is principal , and the ultraproduct is isomorphic to one of the factors .