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!

  • 2
    $\begingroup$ :) $\endgroup$
    – t.b.
    Nov 24, 2011 at 2:31
  • $\begingroup$ @t.b.: :-D. Yes, I haven't forgot it. $\endgroup$
    – Tim
    Nov 24, 2011 at 2:34
  • 1
    $\begingroup$ @Tim: Wikipedia is made by you! I hope you can go there and improve it... ;-) $\endgroup$ Nov 24, 2011 at 2:46
  • $\begingroup$ @AndréCaldas: Yes, and Wiki is my teacher! $\endgroup$
    – Tim
    Nov 24, 2011 at 2:47
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    $\begingroup$ 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 $\mathbb R$. $\endgroup$ Nov 24, 2011 at 3:03


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