A METHOD OF PARTITIONING THE SET OF NATURAL NUMBERS
A METHOD OF PARTITIONING THE SET OF NATURAL NUMBERS

Author(s): Teodor Dumitru Vălcan
Subject(s): Social Sciences, Education, School education
Published by: Editura Eikon
Keywords: set; equivalence relation; partition; natural numbers; irrational numbers;
Summary/Abstract: The didactic experience of teaching - learning Mathematics in the preparatory class (CP) and grades I - IV, even of the implementation of mathematical activities in kindergarten, reveals an important amount of notions, relationships and properties that belong to the programs, but are not always rigorously integrated and presented. Hence the need for notional clarification and ensuring rigor in the use of concepts and arguing / proving statements, properties, theorems and solving exercises or problems. The present paper can achieve a part of this desired. Thus, after a brief presentation of the notions of equivalence relation and partition of a set, the connection between an equivalence relation and a partition and some concrete examples, we will present a very interesting partition of the set N, of the non-zero natural numbers, partition generated by two irrational numbers, but also the equivalence relation generated by this partition. We will also exemplify such situations.

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