In mathematics, the limit inferior and limit superior of a sequence can be thought of as limiting (that is, eventual and extreme) bounds on the sequence...

concept of a limit of a topological net, and is closely related to limit and direct limit in category theory. The limit inferior and limit superior provide...

the two limits of a function as a specified point is approached from below or from above Limit inferior and limit superior Limit of a net Limit point,...

spacePages displaying short descriptions of redirect targets Limit superior and limit inferior – Bounds of a sequencePages displaying short descriptions...

limit inferior, or liminf. See limit superior and limit inferior. If ( X , d ) {\displaystyle (X,d)} is a metric space and there is a Cauchy sequence such...

Limit point Subsequential limit Limit superior and limit inferior Limit of a function Limit of a sequence of sets Limit of a net Pointwise convergence...

Soc. p. 130. ISBN 978-1-4704-2807-5. Retrieved 7 August 2021. Projectively extended real line Semi-differentiability Limit superior and limit inferior...

defined as the difference (possibly infinite) between the limit superior and limit inferior of ( a n ) {\displaystyle (a_{n})} : ω ( a n ) = lim sup n...

common. Moreover, as pointed out in the article about the limit inferior and limit superior, the lim sup x → a {\displaystyle \textstyle \limsup _{x\to...

|f(x)-L|<\varepsilon } . This is the (ε, δ)-definition of limit. The limit superior and limit inferior of a sequence are defined as lim sup n → ∞ x n = lim...