 We now need to introduce another aspect of 19th century mathematics that brought that crucial distinction into focus. The distinction between finiteness and boundedness (and consequently that between infinitude and unboundedness) greatly improved our understanding of issues concerning the structure of space, and what shape a finite, or an infinite space, might take. Recall that for two centuries after Newton, cosmology was developed within the framework of Euclidean infinite space. Such a space is infinite in all directions, it is homogeneous and isotropic—that is, it is the same at all locations and in all directions.