.Open Theories of Multisets and Bags
In a set an object is either a member of not a member.
In a list an object is either in a list at one or more
specific places, or not there at all.
In a $Bag or $MultiSet an object can be in a set 0,1,2,3, or more times.
For S:Sets, Bag(S) ::=$ $FLOW(S->Nat0,+, 0).
For S:Sets, MultiSet(S) ::=$ $FLOW(S->Nat0,+, 0).
I prefer to treat these as special cases of flosets:
ordered sets with an addition operator.
FLOW::=http://www/dick/maths/math_23_Flow_Diagrams.html#flosets
Also compare with Fuzzy Sets where an object may be partly in and partly out
of a set:
.See http://www/dick/maths/math_83_Fuzzy_Sets.html
It is also possible to develop the theory of Bags/multisets independently:
.Hole
.Close Theories of Multisets and Bags