Non-standard analysis

The history of calculus is fraught with philosophical debates about the meaning and logical validity of fluxions or infinitesimal numbers. The standard way to resolve these debates is to define the operations of calculus using epsilon–delta procedures rather than infinitesimals. Non-standard analysis instead reformulates the calculus using a logically rigorous notion of infinitesimal numbers. Non-standard analysis was originated in the early 1960s by the mathematician Abraham Robinson. He wrote: Robinson argued that this law of continuity of Leibniz's is a precursor of the transfer principle. Robinson continued: