Definition talk:Closed Linear Span

I wonder whether it's better to use "\vee" for $\vee$ rather than "\lor" ($\lor$). Yes I know both are the same character, but the latter is specifically "logical or" and there may be good reasons for keeping a distinction. --prime mover 14:17, 21 December 2011 (CST)
 * Sure, \lor was just the one that came to mind first. --Lord_Farin 15:40, 21 December 2011 (CST)

Generalisation
I am quite convinced that the concept can be generalised to arbitrary linear subspaces of vector spaces. I lack a valid reference, though. --Lord_Farin 10:04, 4 January 2012 (CST)

Meaning of "smallest"
TL;DR: The definition with "smallest" does not make much sense. I suggest to merge it with the definition with $\bigcap$.

This occurs often in this type of definitions: what is meant by smallest? AFAIK the only way to define it is as in the definition with $\bigcap$. Otherwise you'd have to prove that there is a smallest set and that it is unique, which is tedious and all those verifications lead to the same as the definition with $\bigcap$. --barto (talk) 04:46, 3 May 2017 (EDT)


 * First I note that "smallest" in this context needs a link. What is intended is to say "of all the sets that have this property, this one is the subset of all of them". (A link to "Definition:Smallest Set" is probably needed here, which itself should probably be changed to "smallest subset") Yes, it is equivalent to the intersection statement, and there is a general statement that probably exists somewhere on this site proving this (if not it ought to).


 * But the fact is that there are source works out there (or so I am informed) which do define this object (and others similar, but particularly that of closure) using the language "smallest", but without stating what is meant by "smallest" and expecting the student to understand it without explanation.


 * One of the aims of is specifically to document such definitions, in order for any student, picking up the threads of an argument from where it is (possibly inadequately) stated in a (possibly substandard) textbook (and there are plenty) and have a pathway through to completely understand what is meant without that nagging doubt.


 * Hence the plan for this page would be to split it into its three subpages, each with its own definition, and a separate page for an equivalence proof. --prime mover (talk) 06:25, 3 May 2017 (EDT)


 * Okay. I will look for that general definition or take care of it if it doesn't exist yet. --barto (talk) 06:50, 3 May 2017 (EDT)
 * I suppose we don't want it to link directly to Definition:Smallest/Ordered Set. A bit too general it seems to me. --barto (talk) 06:53, 3 May 2017 (EDT)


 * No, to "Definition:Smallest Set" like I said. --prime mover (talk) 06:56, 3 May 2017 (EDT)


 * Oh, I see. (I tend to miss things in a text with much information; I guess that's why I like those short and nicely structured definition pages at ) --barto (talk) 07:03, 3 May 2017 (EDT)