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In mathematics, a formal sum, formal series, or formal linear combination may be: *In group theory, an element of a free abelian group, a sum of finitely many elements from a given basis set multiplied by integer coefficients. *In linear algebra, an element of a vector space, a sum of finitely many elements from a given basis set multiplied by real, complex, or other numerical coefficients. *In the study of
series (mathematics) In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). I ...
, a sum of an infinite sequence of numbers or other quantities, considered as an abstract mathematical object regardless of whether the sum converges. *In the study of
power series In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It ...
, a sum of infinitely many monomials with distinct positive integer exponents, again considered as an abstract object regardless of convergence. {{sia