Talk:Union (set theory)

Move issues
Because this page was moved without using the "Move this page" feature and the edit history was later recombined, this history may look odd near 2002 April 6 and 2003 February 7. However, every version saved is in the history at its correct date. -- Toby 00:27 Mar 5, 2003 (UTC)

Definite problem
There is a very clear problem with the picture on this page and/or the picture on the intersection page. If you pay attention they are the same picture. Being as they are opposites, I find it unlikely that the middle section of a Venn Diagram of A and B is both AuB and AnB LFStokols 03:46, 9 March 2007 (UTC) LFStokols
 * So far as it seems, this issue has been resolved. J O R D A N [ talk ] 20:45, 13 June 2008 (UTC)

Infinitary intersection
The article mentions the infinitary intersection; but I think there must be a warning that the "infinitary intersection" of no sets is not defined (unless we accept that it is the class of all sets): $$\bigcap_{x \in \varnothing} x = ?\,$$. Contrast this with the infinitary union, that is defined for all sets. Albmont (talk) 13:19, 15 December 2008 (UTC)

Confusing...
With all the mathematical symbols and language all over the place from the get-go, this article is impossible to follow. Isn't a union just everything that is in all the sets? What more is there to say? --Jubilee♫ clipman 08:01, 9 February 2010 (UTC)

>>>>You are forgetting about the universal set, so it would not be correct to say 'all' sets. 70.117.168.47 (talk) 04:24, 8 January 2013 (UTC)

When a concept from set theory is being discussed I think you should expect mathematical symbols to be used, after all you wouldn't expect a discussion of addition (in the arithmetical sense) to forgo use of the symbol "+" would you? 213.122.23.20 (talk) 23:16, 21 February 2010 (UTC)

"Infinite" unions
The title of section 2.2 "Infinite unions" is misleading, M may be finite. 213.122.23.20 (talk) 23:05, 21 February 2010 (UTC)

Arbitrary? Infinitary? Clarification needed
In section "Arbitrary unions", toward the end the terms "infinitary union" and "infinitary intersection" make an appearance. What is the relationship between "arbitrary" and "infinitary"? Naively I would have expected "infinitary" to be encompassed within "arbitrary", so now I wonder what special point is being made by restricting the last couple of statements ("Intersection distributes over infinitary union" on) to only infinitary. (And are we to assume that the "I" in these two statements is the set of natural numbers?) Gwideman (talk) 21:58, 25 August 2012 (UTC)


 * "infinitary union" and "arbitrary union" are synonyms; a sentence should be added at the beginning of the section saying this, and the usage should be standardized. --JBL (talk) 03:26, 28 August 2012 (UTC)


 * Thanks JBL, that was helpful. Gwideman (talk) 22:50, 30 August 2012 (UTC)

It would also be useful to note other synonyms. I suggest these include unary union (presumably unary in contrast to binary in that it operates on one set, of arbitrarily many other sets, rather than always on two sets), perhaps generalised union, and perhaps cascaded union (implying repeated folding of ordinary binary union; this term seems to have been used in GIS). Cesiumfrog (talk) 21:44, 10 January 2017 (UTC)

"in symbol" definition seems to be wrong
According to the definition
 * $$A \cup B = \{ x: x \in A \text{  or  } x \in B\}$$

for e.g. $$A = \{ 1, 2 \}$$ and $$B = \{ 3, 4 \}$$, the set $$C = \{1, 3 \}$$ should be considered a union of A and B, while it obviously isn't a union of them. — Preceding unsigned comment added by 2A01:4B00:881D:100:8D44:ADCA:4103:BC01 (talk) 01:28, 6 January 2020 (UTC)


 * The notation $$ \{x \colon [\textrm{condition}]\}$$ means the set of all $x$ that satisfy the condition. --JBL (talk) 02:18, 6 January 2020 (UTC)