*note: I had this reviewed by a moderator before posting, so I hope you consider it appropriate to this forum. Hypothetical proposition (of the form “if p, then q” – without asserting the truth of p or q): If space-time S is not infinitely divisible, then space-time S cannot be infinite in extent. Proof: If space-time S is not infinitely divisible, then there exists a smallest possible increment of S, s. [The precise size of s does not matter; it only matters that it is finite.] Since S is built from finite space-time components s, S requires an infinite amount of time (t∞) to become infinite in extent. [note that s is a space-time component, not simply a component of a geometric space.] At any time t, we can assert that t∞ has not yet been reached (since t∞ is infinite). Therefore, at any time t we can assert that space-time S is not infinite in extent. Footnote: the number of dimensions of S (or equivalently, s) does not matter; it only matters that at least one is a time dimension.