Mathematical Structures: History of Multisets

# History of Multisets

 Revision 2 . . July 31, 2004 7:46 pm by Jipsen Revision 1 . . July 9, 2004 10:22 am by Jipsen

Difference (from prior major revision) (no other diffs)

Changed: 28,32c28,29
 \Large Name of class \quad\href{http://math.chapman.edu/cgi-bin/structures?action=edit;id=Template}{edit} % Note: replace "Template" with Name_of_class in previous line \abbreviation{Abbr}

Changed: 35,42c32,33
 A ... is a structure $\mathbf{A}=\langle A,...\rangle$ of type $\langle ...\rangle$ such that $\langle A,...\rangle$ is a \href{Name_of_class.pdf}{name of class} $op_1$ is (name of property): $axiom_1$ $op_2$ is ...: $...$
 A multiset is a structure $\mathbf{A}=\langle A,m\rangle$ where $m$ is a function from $A$ to the class of all cardinals (= initial ordinals). For $a\in A$ the cardinal $m(a)$ is called the multiplicity of $a$.

Changed: 51,52c42,43
 Let $\mathbf{A}$ and $\mathbf{B}$ be ... . A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a function $h:A\rightarrow B$ that is a homomorphism: $h(x ... y)=h(x) ... h(y)$
 Let $\mathbf{A}$ and $\mathbf{B}$ be multisets. A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a function $h:A\rightarrow B$ that preserves multiplicity: $h(m(x))=m(h(x))$

Changed: 78c69
 Classtype & (value, see description) \cite{Ln19xx} \\\hline
 Classtype & (value, see description) \cite{Lastname19xx} \\\hline