Editing Big O notation (section)

== Generalizations and related usages ==
The generalization to functions taking values in any [[normed vector space]] is straightforward (replacing absolute values by norms), where ''f'' and ''g'' need not take their values in the same space. A generalization to functions ''g'' taking values in any [[topological group]] is also possible{{Citation needed|date=May 2017}}.
The "limiting process" {{math|''x'' → ''x''<sub>''o''</sub>}} can also be generalized by introducing an arbitrary [[filter base]], i.e. to directed [[net (mathematics)|nets]] ''f'' and&nbsp;''g''. The ''o'' notation can be used to define [[derivative]]s and [[differentiability]] in quite general spaces, and also (asymptotical) equivalence of functions,
:<math> f\sim g \iff (f-g) \in o(g) </math>
which is an [[equivalence relation]] and a more restrictive notion than the relationship "''f'' is Θ(''g'')" from above. (It reduces to lim ''f'' / ''g'' = 1 if ''f'' and ''g'' are positive real valued functions.)  For example, 2''x'' is Θ(''x''), but {{math|1=2''x'' − ''x''}} is not ''o''(''x'').