Nonstandard Analysis-
Conjuring ghosts of departed quantities
In 1960, Abraham Robinson established the framework in which the
existence of infinitesimals is made precise. He showed that we may
construct enlargements of ultrapowers in
such a way that a mathematical structure contained in the ultrapower is
embedded in the enlargement, and so that true statements about the
embedded structure are true for the enlarged structure, and visa versa
(with suitable interpretation). This construction, when applied to the
real numbers, results in an enlarged totally ordered field containing
infinite as well as infinitesimals along with finite real numbers.
NSA in
economics
NSA
Hypercomplex
Polynomials
Nonstandard
analysis
Hyperreal
Numbers