Set Theory Functions: Multi-Sets

Multi-sets means that we can represent a set as a symbol. We represent a set as a symbol, by putting braces around it {}.

For example, S = {a,b,c,d} and J = {b,d}. We want to put the set J into S, not the elements of the set J into S, that is the difference.

S UNION {J} = S UNION The set J as a symbol = {a,b,c,d} UNION {{b,d}} = {a,b,c,d,{b,d}}.

Notice that symbols b and d occur twice, but since b,d are in a separate set, they have to be counted twice.
A set within a set is called a subset, so {b,d} is a subset of S.