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Results tagged with nonstandard-analysis
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user 11260
Nonstandard analysis is a way of doing calculus and analysis with infinitesimals. The historical approach of Leibniz, Euler, and others to infinitesimal calculus was gradually replaced by epsilon, delta techniques in the context of a real continuum, in the 19th century. It was not until the 1960s that Abraham Robinson developed a theory of a hyperreal continuum that allows for a development of analysis procedurally akin to that of its founders.
10
votes
Accepted
Bibliographic request concerning an article by Bernstein and Robinson
I can identify one individual who scrutinized the Bernstein-Robinson manuscript and established its validity before it was published in PJM:
Paul Halmos, I Want to be a Mathematician: An Automathog …
- 188k
12
votes
Accepted
Has anything (other than what is in the obituary written by M. Noether) survived of Paul Gor...
Paul Gordan's theses were published in De linea geodetica and digitised by Google, from which I reproduce the relevant page:
Translation:
I. The method of functional division, proposed by the res …
- 188k
20
votes
Was Cauchy prescient?
I found this paper by John Cleave, Cauchy, Convergence, and Continuity (1971) quite illuminating.
According to our present-day (Weierstrassian) conception of the
continuum, Cauchy's 1821 theorem …
- 188k
11
votes
Did Lagrange change his mind about infinitesimals?
Gert Schubring's Conflicts Between Generalization, Rigor, and Intuition, page 397 and following, gives a critical assessment of this issue:
- 188k