scholarly journals The Monotonic Sequence Theorem and Measurement of Lengths and Areas in Axiomatic Non-Standard Hyperrational Analysis

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 42
Author(s):  
Yuri N. Lovyagin ◽  
Nikita Y. Lovyagin
Keyword(s):  
Line Segment ◽  
Cauchy Sequence ◽  
Research Method ◽  
Axiomatic Theory ◽  
Real Numbers ◽  
Integral Calculus ◽  
Standard Analysis ◽  
Monotonic Sequence ◽  
Basic Concepts ◽  
Non Standard Analysis

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.

scholarly journals Applications of Non-Standard analysis in Topoi to Mathematical Neurosciences and Artificial Intelligence: Infons, Energons, Receptons (I)

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2048
Author(s):  
Ileana Ruxandra Badea ◽  
Carmen Elena Mocanu ◽  
Florin F. Nichita ◽  
Ovidiu Păsărescu
Keyword(s):  
Mathematical Modeling ◽  
Artificial Intelligence ◽  
Mathematical Model ◽  
Set Theory ◽  
Standard Analysis ◽  
New Methods ◽  
Internal Set ◽  
Human Thinking ◽  
Global Brain ◽  
Non Standard Analysis

The purpose of this paper is to promote new methods in mathematical modeling inspired by neuroscience—that is consciousness and subconsciousness—with an eye toward artificial intelligence as parts of the global brain. As a mathematical model, we propose topoi and their non-standard enlargements as models, due to the fact that their logic corresponds well to human thinking. For this reason, we built non-standard analysis in a special class of topoi; before now, this existed only in the topos of sets (A. Robinson). Then, we arrive at the pseudo-particles from the title and to a new axiomatics denoted by Intuitionistic Internal Set Theory (IIST); a class of models for it is provided, namely, non-standard enlargements of the previous topoi. We also consider the genetic–epigenetic interplay with a mathematical introduction consisting of a study of the Yang–Baxter equations with new mathematical results.

scholarly journals METACOGNITIVE SKILLS ANALYSIS OF STUDENTS IN INTEGRAL CALCULUS PROBLEM SOLVING

2021 ◽  
Vol 12 (2) ◽  
pp. 170
Author(s):  
Nurina Kurniasari Rahmawati ◽  
S B Waluya ◽  
Rochmad Rochmad ◽  
Isti Hidayah
Keyword(s):  
Problem Solving ◽  
Research Method ◽  
Sampling Technique ◽  
Monitoring And Evaluation ◽  
Observation Data ◽  
Metacognitive Skills ◽  
Integral Calculus ◽  
Evaluation Stage ◽  
Three Stages ◽  
Academic Year

This study aims to describe the profile of students' metacognitive skills in solving integral calculus problems seen from the aspects of planning, monitoring and evaluation metacognitive skills. The research method used is descriptive qualitative research methods. The subjects in this study were 3rd semester students who had taken courses or were taking calculus II courses for the 2020/2021 academic year which were carried out using purposive sampling technique. In this study, the instrument used was a test to measure the ability in solving integral calculus problems in the form of essay questions, unstructured interview guidelines, documentation and observation. Data were analyzed in three stages, namely reduction, presentation, and conclusion or verification. The results in this study were students with high problem solving abilities had met the indicators of metacognitive skills, namely the planning, monitoring and evaluation stages. Students with moderate problem-solving abilities have only reached indicators of metacognitive skills, namely the planning and monitoring stages, but have not reached the evaluation stage, while students with low problem-solving abilities have not measured metacognitive skills indicators both at the planning, monitoring and evaluation stages. So that students with high problem solving abilities are more likely to have good metacognitive skills, because students with high problem solving abilities are well organized from planning, monitoring to the evaluation stage.

scholarly journals konsep administrasi pendidikan

2020 ◽  
Author(s):  
Nadia
Keyword(s):  
Driving Force ◽  
Research Method ◽  
Education Administration ◽  
Basic Concepts

This article was created with the aim that readers can understand the basic concepts of education administration. As for this research method, using the existing literature and developing what is obtained from lectures. According to Parajudi Atmosudirjo (1975), administration is the control and driving force of an organization in such a way that the organization comes alive and moves towards the achievement of everything set by the leadership of the organization.

Introduction to the axiomatic theory of elementary functions

2021 ◽  
Author(s):  
Andrey Shishkin
Keyword(s):  
Complex Variable ◽  
Real Variable ◽  
Complex Variables ◽  
State University ◽  
Axiomatic Theory ◽  
Elementary Functions ◽  
State Pedagogical ◽  
Pedagogical Institute ◽  
State Pedagogical Institute ◽  
Basic Concepts

Contains an exposition of the basic concepts and theorems of the axiomatic theory of the basic elementary functions of real and complex variables. The textbook is written on the basis of lectures given by the author for a number of years at the Armavir State Pedagogical University, at the Slavyansk-on-Kuban State Pedagogical Institute and at the branch of the Kuban State University in Slavyansk-on-Kuban. It is intended for students of natural-mathematical profiles of preparation of the direction "Pedagogical education". It can be used in the study of mathematical analysis, the theory of functions of a real variable, the theory of functions of a complex variable, etc.

Sign in / Sign up

Export Citation Format

Share Document