 In the general context of a "G"-valued series, a distinction is made between absolute and unconditional convergence, and the assertion that a real or complex series which is not absolutely convergent is necessarily conditionally convergent (meaning not unconditionally convergent) is then a theorem, not a definition.This is discussed in more detail below.Given a series formula_59 with values in a normed abelian group "G" and a permutation σ of the natural numbers, one builds a new series formula_60, said to be a rearrangement of the original series.