ABSTRACT
The history of classical analysis is perhaps the most investigated part of the history of mathematics, and that is quite natural. Mathematical analysis has been viewed as the “simplest and most universal language—most suitable for expressing the invariable relations of natural phenomena”. One of the basic principles of non-standard analysis is the principle of transfer/translation, according to which every true statement of classical analysts (the classical theory of sets) is true in the non-standard analysis (non-standard theory of sets) too, and conversely. Thus, non-standard analysis appears to be yet another model for that very class of analytical phenomena and relations among them, for which the model of classical analysis was built. After the construction of non-standard analysis, classical analysis of the 19th century ceased to be the only correct analytical construction, its universalization and absolutization appeared to be illegitimate forms of activities.
