Talk:Union is Associative

Yes it may also be a Set Theory proof but Union is a sub-category of Set Theory so it goes in there not in Set Theory. Otherwise what would be the point of defining a hierarchy in the first place?--Matt Westwood 06:40, 18 August 2008 (UTC)

You put it in both; that way, you get a big pool of "set theory" topics which is narrowed down as you decline through the subcategories. You want to have both the pool and the organized tree, right? -Dan

Would this be a suitable place to present also:

$\bigcup_n (A_n\cup B) = (\bigcup_n A_n) \cup B$

$\bigcup_n (A_n\cup B_n) = \bigcup_n A_n \cup \bigcup_n B_n$

where the former instantiates the latter? It is a bit like 'union distributes over union' but it also has something of associativity in it, especially the former. --Lord_Farin 07:06, 19 May 2012 (EDT)

I'd be tempted to put it in a separate page. Then it can be linked to directly where needed. There's a general result in the abstract algebra page for a general associative and commutative operation which this mirrors directly, and I'd be tempted to make it a direct application of that, as to do a rigorous job on it requires induction. --prime mover 07:14, 19 May 2012 (EDT)

Fair enough; note though that set union is not a finitary operation. So I doubt that direct application is possible. Better to do the double inclusion, I think. Let's move the discussion to Union Distributes over Union (and, for that matter, Intersection Distributes over Intersection). --Lord_Farin 07:26, 19 May 2012 (EDT)