Almost all

Throughout mathematics, "almost all" is sometimes used to mean "all (elements of an infinite set) except for finitely many".

[3] Similarly, "almost all" can mean "all (elements of an uncountable set) except for countably many".

[8] The real line can be thought of as a one-dimensional Euclidean space.

In the more general case of an n-dimensional space (where n is a positive integer), these definitions can be generalised to "all points except for those in a null set"[sec 3] or "all points in S except for those in a null set" (this time, S is a set of points in the space).

[20][22] Sometimes, the latter definition is modified so that the graph is chosen randomly in some other way, where not all graphs with n vertices have the same probability,[21] and those modified definitions are not always equivalent to the main one.

[20] Example: In topology[24] and especially dynamical systems theory[25][26][27] (including applications in economics),[28] "almost all" of a topological space's points can mean "all of the space's points except for those in a meagre set".

Some use a more limited definition, where a subset contains almost all of the space's points only if it contains some open dense set.