Editing Arithmetization of analysis (section)

==Legacy==
An important spinoff of the arithmetization of analysis is set theory. Naive set theory was created by Cantor and others after arithmetization was completed as a way to study the singularities of functions appearing in calculus. 

The arithmetization of analysis had several important consequences:
* the widely held belief in the banishment of [[infinitesimal]]s from mathematics until the creation of [[non-standard analysis]] by [[Abraham Robinson]] in the 1960s, whereas in reality the work on non-Archimedean systems continued unabated, as documented by P. Ehrlich;
* the shift of the emphasis from [[geometry|geometric]] to [[algebra]]ic reasoning: this has had important consequences in the way mathematics is taught today;
* it made possible the development of modern [[measure theory]] by [[Henri Lebesgue|Lebesgue]] and the rudiments of [[functional analysis]] by [[David Hilbert|Hilbert]]; 
* it motivated the currently prevalent philosophical position that all of mathematics should be derivable from [[logic]] and set theory, ultimately leading to [[Hilbert's program]], [[Kurt Gödel|Gödel]]'s theorems and [[non-standard analysis]].