In our representations of the world, especially in physics, (mathematical) infinities play a crucial role. The continuum of the real numbers, \(\Re\), as a representation of time or of one-dimensional space is surely the best known example and, by extension, the \(n\)-fold cartesian product, \(\Re^{n}\), for \(n\)-dimensional space. However, these same infinities also cause problems. One just has to think about Zeno’s paradoxes or the present-day continuation of that discussion, namely the discussion about supertasks, to see the difficulties (see the entry on supertasks in this encyclopedia for a full treatment). Hence, it is a very tempting idea to investigate whether it is possible to eliminate these infinities and still be able to do physics. The first step towards an answer to that question is to examine whether or not a discrete geometry is possible that can approximate classical continuous geometry as closely as possible. For, if such is the case, the latter geometry can easily be replaced by a discrete version in any physical theory that makes use of this particular mathematical background.