Formal sum

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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), a sum of an infinite sequence of numbers, considered as an abstract mathematical object regardless of whether the sum converges.
  • In the study of power series, a sum of infinitely many monomials with distinct positive integer exponents, again considered as an abstract object regardless of convergence.