In
mathematics, the affinely extended real number system is obtained from the
real number
In mathematics, a real number is a number that can be used to measure a ''continuous'' one-dimensional quantity such as a distance, duration or temperature. Here, ''continuous'' means that values can have arbitrarily small variations. Every ...
system
by adding two
infinity elements:
and
where the infinities are treated as actual numbers. It is useful in describing the algebra on infinities and the various
limiting behaviors in
calculus
Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithm ...
and
mathematical analysis
Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series (m ...
, especially in the theory of
measure and
integration. The affinely extended real number system is denoted
or