Open AccessTeoretyczne podstawy dzielenia z resztą liczb naturalnych wraz z uwagami o dzieleniu z resztą liczb całkowitych, wymiernych i rzeczywistych
Author(s) -
Antoni Chronowski
Publication year - 2020
Publication title -
annales universitates paedagogicae cracoviensis. studia ad didacticam mathematicae pertinentia
Language(s) - English
Resource type - Journals
eISSN - 2450-341X
pISSN - 2080-9751
DOI - 10.24917/20809751.11.4
Subject(s) - remainder , natural number , division (mathematics) , generalization , notation , mathematics , arithmetic , rational number , combinatorics , discrete mathematics , mathematical analysis
In this article, I analyze the theoretical foundations of the division with remainder in the arithmetic of natural numbers. As a result of this analysis I justify that the notation a:b=c r s, where a, b, c, s are natural numbers and r denotes, is correct at school mathematics level and does not lead to a contrediction suggested by the author of the article (Semadeni, 1978). As a generalization of the division with remainder of natural numbers, I consider the division with remainder of integers, rational and real numbers.