We relate a category of models A to a category of more realistic objects B which the models approximate. For example polyhedra can approximate smooth shapes in the infinite limit…. In Borsuk’s geometric shape theory, A is the homotopy category of finite polyhedra, and B is the homotopy category of compact metric spaces.
—-Jean-Marc Cordier and Timothy Porter, Shape Theory
(I rearranged their words liberally but the substance is theirs.)
prod( factorial( 1/ 1:10e4) ) to see the volume of Hilbert’s cube → 0.