A Relation on domains D1 x D2 x D3 x ... x Dn:
is potentially infinite so long as at least one domain is infinite
is potentially uncountable so long as at least one domain is uncountable
(see RelationalModel).
A FiniteRelation is a Relation possessing the quality of being finite. FiniteRelations have nice qualities for use in DataBases. In particular, it is possible to compute a list of all things in a finite relation, and it is possible to represent the relation as a simple list (aka. a 'table'). RelationalAlgebra operations over FiniteRelations, excepting Inverse, are closed.
All FiniteRelations are also CountableRelation.