Alternating series have the simplest of sign patterns. What about series with more complicated patterns? By inspecting the alternating series test closely, we find a theorem that applies to more complicated sign patterns, and beyond.

If a series of real numbers converges absolutely, then it converges. The usual proof requires completeness in the form of the Cauchy criterion. Failing completeness, the result is false. We provide examples of rational series that illustrate this point. The Cantor set appears in connection with one of the examples.