Editing Transfer principle (section)

==History==
An incipient form of a transfer principle was described by [[Gottfried Wilhelm Leibniz|Leibniz]] under the name of "the [[Law of Continuity]]".<ref name="Keisler2000">{{cite web|last1=Keisler|first1=H. Jerome|title=Elementary Calculus: An Infinitesimal Approach|url=http://www.math.wisc.edu/~keisler/calc.html|page=902}}</ref> Here [[infinitesimal]]s are expected to have the "same" properties as appreciable numbers. The transfer principle can also be viewed as a rigorous formalization of the [[principle of permanence]]. Similar tendencies are found in [[Augustin-Louis Cauchy|Cauchy]], who used infinitesimals to define both the [[continuous function|continuity of functions]] (in [[Cours d'Analyse]]) and a form of the [[Dirac delta function]].<ref name="Keisler2000"/>{{rp|903}}

In 1955, [[Jerzy Łoś]] proved the transfer principle for any [[hyperreal number]] system.  Its most common use is in  [[Abraham Robinson]]'s [[nonstandard analysis]] of the [[hyperreal number]]s, where the transfer principle  states that any sentence expressible in a certain formal language that is true of [[real number]]s is also true of hyperreal numbers.