Talk:Multiset

message: Article currently says:
:Within set theory, a multiset may be formally defined as a 2-tuple(A, m) where A is some set and m : A → N≥1 is a function from A to the set N≥1 = {1, 2, 3, ...} of positive natural numbers. The set A is called the underlying set of elements.
As stated, this excludes the (rather natural) possibility of elements with infinite multiplicity.
I see that this was the very first complaint on this talk page, and references were even given, but nothing seems to have been done about it.  This strikes me as rather serious.  If you're allowing infinite sets, then I can't see much point in disallowing infinite multiplicities too. --Trovatore (talk) 01:54, 19 April 2012 (UTC)
replies: text: "If you're allowing infinite sets ..." In fact it looks to me like everything in the article is about finite multisets (i.e., this is an article about combinatorics, with a little bit of set theoretic exposition thrown in to help make it less comprehensible ;) ).  One could write an article about multisets including infinite ones, but it seems like in that case it would still be good to have an article like this one about only the finite aspects.  --Joel B. Lewis (talk) 03:37, 19 April 2012 (UTC)
replies: text: Well, there's nothing in the article that says it's about finite multisets, and set theory is really not that interesting/useful until you get to infinite sets, except as you say to make things less comprehensible.  It's true that only one example comes to mind where I came across multisets in set theory itself, but still, the most natural notion of multiset does not seem to be restricted to the finite case. --Trovatore (talk) 03:53, 19 April 2012 (UTC)
thread_title:  Infinite multiplicity again 

message: Wouldn't a simple application be, say, the roots of (x+4)(x-1)^2?  In set notation it's {−4, +1}, but multisets allow you to show multiplicity of roots, like {−4, +1, +1}.  — Preceding unsigned comment added by 68.198.133.72 (talk) 20:53, 7 July 2014 (UTC)
thread_title:  Applications section 

message: It can be easily proven that \sum_{i=0}^k\left(\!\!\binom{n}{i}\!\!\right)=\left(\!\!\binom{n+1}{k}\!\!\right). I think this formula should be included in the article. Aside from its intrinsic interest, it comes handy when studying dimensions of some subspaces of vector spaces and/or problems related to polynomials.
Example 1: If we consider a polynomial of degree d in n variables along with all its first k-derivatives, this formula computes, from the number of derivatives of order i for each i, the total number of polynomials arising in the system.
Example 2: Since the homogeneous polynomials of degree i in n variables over a field form a subspace H(n,i) of dimension \left(\!\!\binom{n}{i}\!\!\right), this formula shows that H(n+1,k) is isomorphic to H(n,0)\oplus\cdots\oplus H(n,k), what can also be inferred from the homogeneization process.
What do you think?
Jose Brox (talk) 10:49, 21 August 2018 (UTC)
thread_title:  Interesting elementary formula 

message: A correspondent mathematician questions the whole concept of multisets, basically saying it is poorly defined. He therefore cannot believe Dedekind would have had anything to do with them (Reference 11). Does anybody here happen to know the page number where Dedekind describes/uses multisets in his book?
Failing that, is there some authoritative source which defines this concept, preferably a book on set theory? It seems that discrete maths does not count for my correspondent; it is probably not real maths ;-) KarlFrei (talk) 16:59, 11 December 2018 (UTC)
replies: text: The definition in the article of a multiset being a pair of a set and a function of this set to positive integers is perfectly accurate, and cannot be qualified as poor. For an authoritative source, Knuth's book (reference 2 of the article) is the best possible reference. This book is sufficiently important to have an article in Wikipedia, and has often been qualified as the "Bible of discrete mathematics". Your correspondent is free to consider that some part of mathematics is not really mathematics, but this is clearly not the opinion of American Mathematical Society, which includes discrete mathematics in its subject classification. I guess that your correspondent consider as not "counting" everything that they does not know ;-) D.Lazard (talk) 19:03, 11 December 2018 (UTC)
replies: text: Sorry for my lack of reply till now. Thank you! KarlFrei (talk) 07:44, 15 February 2019 (UTC)
thread_title:  Dedekind source