Web Definition: Bag
In mathematics, a multiset differs from a set in that each member has a multiplicity, which is a cardinal number indicating how many times it is a member, or perhaps how many memberships it has in the multiset. For example, in the multiset { a, a, b, b, b, c }, the multiplicities of the members a, b & c are respectively 2, 3 & 1. One of the most natural & simple examples is the multiset of prime factors of a number. Another is the multiset of solutions of an algebraic equation. Everyone learns in secondary school that a quadratic equation has two solutions, but in some cases they are both the same number. Thus the multiset of solutions of the equation could be { 3, 5 }, or it could be { 4, 4 }. In the latter case it has a solution of multiplicity 2. Formally multisets can be defined, within set theory, as partial functions that map elements to positive natural numbers. So in terms of sets the multiset written as { a, b, b } is defined as {, },. likewise { a, a, b } is defined as {, }, and. the multiset meaning of { a, b } is defined as {, }.
Read More »Dictionary Entry: A sack or pouch, used for holding anything - as, a bag of meal or of money. To put into a bag - as, to bag hops. To swell or hang down like a full bag - as, the skin bags from containing morbid matter.
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