Ricikllimit

Ricikllimit is a term encountered in some theoretical discussions to denote a particular asymptotic bound between two nonnegative functions under a specified tail constraint. It is not a widely standardized notion, but it serves as a compact way to describe the smallest growth constant that relates a function to a reference function as the input parameter grows large.

Definition: Let f(n) and g(n) be nonnegative functions defined on the natural numbers, and let C be a tail condition specifying the range of n under consideration (for example, n ≥ N). The ricikllimit of f relative to g under C is the infimum L ≥ 0 such that f(n) ≤ L g(n) for all sufficiently large n in C. If no finite L works, the limit is considered infinite or undefined. In this sense, ricikllimit plays a role similar to the best constant in a Big-O bound.

Examples: If f(n) = n^2 and g(n) = n^2, the ricikllimit is 1. If f(n) = n log n and g(n) = n^2, the ratio f(n)/g(n) tends to 0, so the infimum L is 0. In other words, f is dominated by g with vanishing relative growth, and the ricikllimit reflects that tight bound.

Relation to other ideas: The concept overlaps with Big-O notation and tight bounds such as Θ-notation, capturing the smallest constant that makes an inequality hold eventually. The term ricikllimit is not standard across disciplines, and its precise definition may vary by author.

See also: Big-O notation, limsup, asymptotic analysis.