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In mathematics, the multiplicity of a member of a multiset is the number of times it appears in the multiset. For example, the number of times a given polynomial has a root at a given point is the multiplicity of that root.
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula.
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. More generally, the fundamental theorem of algebra asserts that the complex solutions of a polynomial equation of degree d always form a multiset of cardinality d.
Multiplicity (chemistry), multiplicity in quantum chemistry is a function of angular spin momentum; Multiplicity (informatics), a type of relationship in class diagrams for Unified Modeling Language used in software engineering; Multiplicity (mathematics), the number of times an element is repeated in a multiset
1684 (deriving from use of colon to denote fractions, dating back to 1633) middle dot (for multiplication ) 1698 (perhaps deriving from a much earlier use of middle dot to separate juxtaposed numbers)
Note that even simple equations like = are solved using cross-multiplication, since the missing b term is implicitly equal to 1: =. Any equation containing fractions or rational expressions can be simplified by multiplying both sides by the least common denominator.
Modern computer algebra systems, as well as many scientific and graphing calculators, allow for "pretty-printing", that is, entry of equations such that fractions, surds and integrals, etc. are displayed in the way they would normally be written. Such calculators are generally similar in appearance to those using infix notation, but feature a ...
Microsoft Math Solver (formerly Microsoft Mathematics and Microsoft Math) is an entry-level educational app that solves math and science problems. Developed and maintained by Microsoft , it is primarily targeted at students as a learning tool.