This simple example illustrates that the various versions of the Baker–Campbell–Hausdorff formula, which give expressions for "Z" in terms of iterated Lie-brackets of "X" and "Y", describe "formal" power series whose convergence is not guaranteed. Thus, if one wants "Z" to be an actual element of the Lie algebra containing "X" and "Y" (as opposed to a formal power series), one has to assume that "X" and "Y" are small. Thus, the conclusion that the product operation on a Lie group is determined by the Lie algebra is only a local statement. Indeed, the result cannot be global, because globally one can have nonisomorphic Lie groups with isomorphic Lie algebras.