Talk:Supremum of Suprema

"as soon as one of these quantities exists" - i.o.w if there is no supremum for $T_i$ the result still holds? I'm not convinced by the proof, by dint of the first few lines:

"Suppose that $s = \sup \bigcup \mathbb T \in S$.

By Set is Subset of Union, $T \subseteq \bigcup \mathbb T$ for all $T \in \mathbb T$.

Hence by Supremum of Subset:


 * $\forall T \in \mathbb T: \sup T \preceq s$"

That last line is not true if if there is no supremum for $T_i$.

Is there something I'm missing? --prime mover (talk) 06:19, 3 January 2013 (UTC)


 * You may have missed the third line of presuppositions. All $T \in \mathbb T$ admit suprema, but this does not imply the two large suprema exist. --Lord_Farin (talk) 16:11, 3 January 2013 (UTC)

Technical note?
Do we actually need one here? There doesn't seem to be anything particularly difficult or unexpected about the $\LaTeX$ involved... --Dfeuer (talk) 05:43, 13 January 2013 (UTC)


 * I would suggest that, unless every single page on this site be amended to add the recommended $\LaTeX$ source code, then no, the "Technical note" can be safely omitted - as now.


 * Whether we do want to add a demand to the house rules that "every page must have a technical note appended to the bottom" is a question which I am frightened to ask because of the work which will then devolve to me to do should the answer be in the affirmative. --prime mover (talk) 09:34, 13 January 2013 (UTC)


 * Okay, fine, I wasn't sure anyway. I removed it. --abcxyz (talk) 15:30, 13 January 2013 (UTC)