Talk:Multiset
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[edit] Why stop at finite cardinals?
Formally multisets can be defined, within set theory, as partial functions that map elements to positive natural numbers.
- Stupid question, but why stop at finite cardinals? Why can't a multiset be defined as a map from a (normal) set into Card? Why can't elements "occur infinitely many times" as members?
- Would be a different concept. Charles Matthews 13:36, 4 Apr 2005 (UTC)
- The reason I ask is the following: at the article graph, they say a multigraph is a graph where the edge set is a multiset. This doesn't jive with the category way of thinking of a directed multigraph as a precategory, where with a precategory, there is no restriction on the number of morphisms from one object to another, conceivably, there could be infinitely many distinct such morphisms. So, in this case, "multiset" as defined here isn't broad enough a concept to use for defining "multigraph" (or directed multigraph).
- On another note, why partial function and not just a function? Surely, 1 is a positive natural number. -- Fropuff 16:23, 2005 May 27 (UTC)
[edit] References, size and set constructor notation?
I've been writing a paper which uses the concept of multiset. It fits very well to the problem, that is why.
First, I think I need a reference for the multiset in which all of these defs are given for curious readers. I just remembered that there is not much focus on multisets in computer science, and I am looking for a good reference for that. So, references would be appreciated.
Secondly, can I use | x | to denote the size of multiset x?
Third, I want to adapt the set constructor notation {x:P(x)} for defining certain multisets. Should I be talking explicitly about the representation (A,m), e.g. 
or are there other ways of defining multisets?
--Exa 23:12, 13 November 2005 (UTC)
[edit] polynomial notation
The article says:
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- The infinite multiset of finite multisets of elements from the multiset x2 is
Why is the infinite multiset of finite multisets of elements from the multiset {x, x} different from the infinite multiset of finite multisets of elements from the multiset {x}? Michael Hardy 23:45, 21 February 2006 (UTC)
Oh -- I see: it said
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- "the infinite multiset of finite multisets"
and NOT
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- "the infinite set of finite multisets"
OK, as Emily Litella would say....
Michael Hardy 23:47, 21 February 2006 (UTC)
- Thanks for your improvements. I agree that the text is tricky. I will think about how to make it clearer. Bo Jacoby 07:18, 22 February 2006 (UTC)
[edit] Definition where A is fixed and m(x) can equal zero
My supervisor suggested that A should be a fixed universe of elements and m be a function which can take zero values. This mean e.g. that a subset of (A,m) would be (A,n) where n(x) <= m(x) for all x. Is there a reference for the way Wikipedia currently defines multisets? -- Gmatht 01:09, 17 April 2006 (UTC)
- As the two definitions lead to the same concept, it doesn't really matter which one to chose. But the concept of an element of a multiset in one definition is element of the set, and in the other definition element of the set with nonzero multiplicity. The latter statement seems more complicated to me, but your supervisor may like it. Also the idea of a fixed universe of elements either limits the definition (because a larger fixed universe extends the definition), or makes matematicians talk unintelligibly about category theory for several minutes. Bo Jacoby 20:02, 17 April 2006 (UTC)
[edit] size, length or cardinality
The article defines "the size or length of the multiset (A, m)". The word "length" is not commonly used in this sense, to the best of my knowledge. The article set uses the word cardinality. Bo Jacoby 10:04, 24 July 2006 (UTC)
[edit] Multiset coefficient wrong in example?
In the example it shows the multiset coefficient as:
I think that should instead be:
Since it's been this way since the original author added it over two years ago, it seems I must be wrong, but it sure doesn't look correct to me. —Doug Bell talk•contrib 06:23, 9 November 2006 (UTC)
