addisjoner

Addisjoner, or addition, is a fundamental mathematical operation that combines two elements to produce a sum. In its simplest form it adds numbers, but the concept extends broadly to many mathematical objects, including vectors, matrices, polynomials, and functions. Additions are used to compute totals, accumulate quantities, and form the basis for larger constructions in algebra and analysis.

Notation and core properties are central to understanding addition. The symbol + denotes the operation, so the sum of a and b is written as a+b. For familiar number systems such as integers, rationals, reals, and complexes, addition is closed, meaning the result stays in the same set. It is commutative (a+b=b+a) and associative (a+(b+c)=(a+b)+c). There exists an additive identity, 0, such that a+0=a for any a, and every element has an additive inverse, −a, with a+(−a)=0. In specific contexts addition is performed componentwise, such as vector addition (a1,a2,...)+(b1,b2,...) = (a1+b1, a2+b2, ...), or matrix addition, which is defined entrywise.

Extensions and applications broaden the scope of addition. Infinite sums, or series, require a notion of convergence to yield meaningful results. In abstract algebra, addition is the primary binary operation in abelian groups and is compatible with scalar multiplication in vector spaces. Addition underpins computational methods, data aggregation, and numerous theoretical frameworks across mathematics, science, and engineering.