Nearlimit
Nearlimit is a term used informally in mathematics and related disciplines to denote a value that is approached by a sequence or function values but is not necessarily the limit of the entire sequence. In formal terms, a real number L is a near-limit (often called a limit point or accumulation point in standard terminology) of a sequence (a_n) if there exists a subsequence (a_{n_k}) that converges to L. The full sequence may fail to converge or may converge to a different value.
Properties: Near-limits depend only on accumulation behavior, not on the whole-sequence limit. The set of all
Examples: 1) a_n = (-1)^n has near-limits -1 and 1. 2) a_n = sin(n) has a full interval of
Origins and usage: The term near-limit is used in some teaching contexts to help distinguish convergence from
See also: Limit, Accumulation point, Cluster point, Limit point.