Mathematical Structures: History of Multisets

History of Multisets

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}

\Large Multisets
\quad\href{http://math.chapman.edu/cgi-bin/structures?action=edit;id=Multisets}{edit}

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

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