Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

From Wikipedia:

Let $Y$ be a partially ordered set which is also a topological space and a complete lattice so that the suprema and infima always exist. For a set $X ⊆ Y$, define $$ \liminf X := \inf \{ x \in Y : x \text{ is a limit point of } X \}\, $$ $$ \limsup X := \sup \{ x \in Y : x \text{ is a limit point of } X \}\, $$

I wonder if this definition is consistent in some way with the informal interpretation of $\limsup$ as $\inf \sup$, and of $\liminf$ as $\sup \inf$, or just another case that you "don't know why Wikipedia writes what it writes"? Thanks!

share|cite|improve this question
:) – t.b. Nov 24 '11 at 2:31
@t.b.: :-D. Yes, I haven't forgot it. – Tim Nov 24 '11 at 2:34
@Tim: Wikipedia is made by you! I hope you can go there and improve it... ;-) – André Caldas Nov 24 '11 at 2:46
@AndréCaldas: Yes, and Wiki is my teacher! – Tim Nov 24 '11 at 2:47
Also, the grafted-on note that "neither the limit inferior nor the limit superior of a set must be an element of the set" simply cannot be right. Nothing even slightly like it is true for the standard concepts in $\mathbb R$. – Henning Makholm Nov 24 '11 at 3:03

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.