title: The Monotonic Sequence Theorem and Measurement of Lengths and Areas in Axiomatic Non-Standard Hyperrational Analysis
metadata.name: dc.contributor.author
metadata.value: Lovyagin, Yuri Nikitich
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Lovyagin, Nikita Yurjevich
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2019-07-02T09:24:39Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2019-07-02T09:24:39Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2019-04-10
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Lovyagin, Y.N.; Lovyagin, N.Y. The Monotonic Sequence Theorem and Measurement of Lengths and Areas in Axiomatic Non-Standard Hyperrational Analysis. Axioms 2019, 8, 42.
metadata.lang: en_GB
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/15852
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: This paper lies in the framework of axiomatic non-standard analysis based on the non-standard arithmetic axiomatic theory. This arithmetic includes actual infinite numbers. Unlike the non-standard model of arithmetic, this approach does not take models into account but uses an axiomatic research method. In the axiomatic theory of non-standard arithmetic, hyperrational numbers are defined as triplets of hypernatural numbers. Since the theory of hyperrational numbers and axiomatic non-standard analysis is mainly published in Russian, in this article we give a brief review of its basic concepts and required results. Elementary hyperrational analysis includes defining and evaluating such notions as continuity, differentiability and integral calculus. We prove that a bounded monotonic sequence is a Cauchy sequence. Also, we solve the task of line segment measurement using hyperrational numbers. In fact, this allows us to approximate real numbers using hyperrational numbers, and shows a way to model real numbers and real functions using hyperrational numbers and functions.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: en
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: MDPI
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Axioms> 2019 8(2);42
metadata.lang: -
metadata.name: dc.title
metadata.value: The Monotonic Sequence Theorem and Measurement of Lengths and Areas in Axiomatic Non-Standard Hyperrational Analysis
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: axioms-08-00042.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/15852/1/axioms-08-00042.pdf
resources.format: Adobe PDF
resources.size: 288,23 kB