Standard Part Function

In non-standard analysis, the standard part function is a function from the limited (finite) hyperreals to the reals. It associates to every such hyperreal, the unique real infinitely close to it. As such, it is a mathematical implementation of the historical concept of adequality introduced by Pierre de Fermat. It can also be thought of as a mathematical implementation of Leibniz's Transcendental Law of Homogeneity. The standard part function was first defined by Abraham Robinson as a key ingredient in defining the concepts of the calculus, such as the derivative and the integral, in non-standard analysis. The latter theory is a rigorous formalisation of calculations with infinitesimals. The standard part of x is sometimes referred to as its shadow.