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