Non-nonstandard analysis: Real infinitesimals
type: Item
instance of: scholarly article
title: Non-nonstandard analysis: Real infinitesimals
zbMATH Open document ID: 0932.26014
DOI: 10.1007/BF03024834
author: James Henle
published in: The Mathematical Intelligencer
publication date: 2000-02-23T00:00:00Z
review text: The author reconsiders, as he says, the pre-nonstandard approach initiated by C. Schmieden and the reviewer in 1958. Real sequences defined for almost all subscripts represent the elements of the number system, and infinitesimals are represented by sequences tending to zero. The basic theorems on derivatives, integrals, and continuity are obtained. (Since zero divisors exist, denominators must be avoided, and some of the proofs here are not correct).
reviewed by: Detlef Laugwitz
Mathematics Subject Classification ID: 26E35
zbMATH DE Number: 1283654
zbMATH Keywords: nonstandard analysis
zbMATH Keywords: infinitesimals
MaRDI profile type: Publication
cites work: Q4099541
cites work: Q4342626
cites work: Q3801804
cites work: Anwendungen unendlich kleiner Zahlen. II. Ein Zugang zur Operatorenrechnung von Mikusinski.
cites work: Non-standard analysis
cites work: Eine Erweiterung der Infinitesimalrechnung
full work available at URL: https://doi.org/10.1007/bf03024834
OpenAlex ID: W1978048820
description: scientific article; zbMATH DE number 1283654