formal sum

A 'formal sum' is a symbolic representation of a sum in mathematics, often used in abstract algebra and related fields.

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Definition

C1General Mathematics

(technical, academic)An expression that represents a sum of elements symbolically, without requiring the sum to converge or be numerically evaluated.

Example

  • In many mathematical proofs, a formal sum allows for manipulation of series without considering their convergence.

C2Group Theory

(technical, academic)An element of a free abelian group expressed as a sum of basis elements with integer coefficients.

Example

  • A formal sum in group theory can be written as a combination of group elements with integer coefficients.

C2Linear Algebra

(technical, academic)An element of a vector space represented as a sum of basis elements with coefficients from a specified field.

Example

  • In linear algebra, a formal sum can be used to represent a vector as a linear combination of basis vectors.

C2Series and Power Series

(technical, academic)An ordered sum of terms, often infinite, treated as an abstract mathematical object without regard to convergence.

Example

  • When dealing with power series, mathematicians often use formal sums to handle infinite series abstractly.

Similar

Terms that have similar or relatively close meanings to "formal sum":

sum totalclosed formformal semanticsdirect sumformal logicsumming upsum up