  In this note, we survey two instances in the representation theory of
finite-dimensional algebras where the quantity of a type of structures is
intimately related to the size of those same structures. More explicitly, we
review the fact that (1) a finite-dimensional algebra admits only finitely many
indecomposable modules up to isomorphism if and only if every indecomposable
module is finite-dimensional; (2) the category of modules over a
finite-dimensional algebra admits only finitely many torsion classes if and
only if every torsion class is generated by a finite-dimensional module.
