Limitrelated

Limitrelated is an informal term used in mathematics to describe properties, objects, or results that are defined or characterized through limiting processes. It is not a standard technical term, but is sometimes employed to group ideas that inherently involve taking limits, such as convergence of sequences or functions, and asymptotic behavior.

The scope of limitrelated includes limits of sequences and functions, various modes of convergence (pointwise, uniform), limit superior and limit inferior, and limit theorems that describe stability and transfer of properties in the limit. It also encompasses limit operations in extended contexts, such as limits of sums, products, or integrals, under appropriate hypotheses.

Examples illustrate the usage: a sequence (a_n) with lim a_n = L is limitrelated by its defining limit; a function f that has a limit as x approaches a; the interchange of limit and integral under dominated convergence; the limit of a series defined as the limit of its partial sums.

Because limitrelated is informal, precise definitions vary by author, and the term is mainly a pedagogical tool to emphasize the unifying role of limits across topics in analysis. It does not replace standard terminology, and it is usually supplemented with explicit statements about the specific limit concept being used.

See also: limit (mathematics), convergence, asymptotic analysis, continuity, epsilon-delta definitions.