In mathematics, the creation and definition of new concepts is the first step in opening up a new field of research. Traditionally this step originated from intuition by a process of observation, analysis and abstraction. This article will show a general method by which most of the common notions of number theory, geometry, topology, etc., can be introduced in one and the same particular way. Therefore, we only need some of the tools of naïve set theory: a set of terms to which we apply an equivalence relation. This equivalence relation induces a partition of the terms with which we can consequently associate new concepts. By using this method’s ‘machine’ in an abstract way on arbitrary sets of terms we can create new notions at will, as we will show in this article, for instance, for bidecimal numbers of different kinds. The fact that we reverse the usual procedure of intuition before abstraction, doesn’t mean that we only create esoteric objects without any meaning. On the contrary, their abstract nature precisely provides our imagination with many possibilities for several interpretations in models in which they become useful. So, for example, we can use our bidecimal numbers to define elementary transformations on a cylinder or on a pile of tori.
DOI | 10.11648/j.dmath.20210601.13 |
Published in | International Journal of Discrete Mathematics (Volume 6, Issue 1, June 2021) |
Page(s) | 15-22 |
Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Equivalence Relation, Partition, Mapping, Model, Bidecimal Number of the First Kind, Bidecimal Number of the Second Kind
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APA Style
Rik Verhulst. (2021). A ‘Machine’ for Creating Mathematical Concepts in an Abstract Way, Bidecimal Numbers. International Journal of Discrete Mathematics, 6(1), 15-22. https://doi.org/10.11648/j.dmath.20210601.13
ACS Style
Rik Verhulst. A ‘Machine’ for Creating Mathematical Concepts in an Abstract Way, Bidecimal Numbers. Int. J. Discrete Math. 2021, 6(1), 15-22. doi: 10.11648/j.dmath.20210601.13
AMA Style
Rik Verhulst. A ‘Machine’ for Creating Mathematical Concepts in an Abstract Way, Bidecimal Numbers. Int J Discrete Math. 2021;6(1):15-22. doi: 10.11648/j.dmath.20210601.13
@article{10.11648/j.dmath.20210601.13, author = {Rik Verhulst}, title = {A ‘Machine’ for Creating Mathematical Concepts in an Abstract Way, Bidecimal Numbers}, journal = {International Journal of Discrete Mathematics}, volume = {6}, number = {1}, pages = {15-22}, doi = {10.11648/j.dmath.20210601.13}, url = {https://doi.org/10.11648/j.dmath.20210601.13}, eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.dmath.20210601.13}, abstract = {In mathematics, the creation and definition of new concepts is the first step in opening up a new field of research. Traditionally this step originated from intuition by a process of observation, analysis and abstraction. This article will show a general method by which most of the common notions of number theory, geometry, topology, etc., can be introduced in one and the same particular way. Therefore, we only need some of the tools of naïve set theory: a set of terms to which we apply an equivalence relation. This equivalence relation induces a partition of the terms with which we can consequently associate new concepts. By using this method’s ‘machine’ in an abstract way on arbitrary sets of terms we can create new notions at will, as we will show in this article, for instance, for bidecimal numbers of different kinds. The fact that we reverse the usual procedure of intuition before abstraction, doesn’t mean that we only create esoteric objects without any meaning. On the contrary, their abstract nature precisely provides our imagination with many possibilities for several interpretations in models in which they become useful. So, for example, we can use our bidecimal numbers to define elementary transformations on a cylinder or on a pile of tori.}, year = {2021} }
TY - JOUR T1 - A ‘Machine’ for Creating Mathematical Concepts in an Abstract Way, Bidecimal Numbers AU - Rik Verhulst Y1 - 2021/05/26 PY - 2021 N1 - https://doi.org/10.11648/j.dmath.20210601.13 DO - 10.11648/j.dmath.20210601.13 T2 - International Journal of Discrete Mathematics JF - International Journal of Discrete Mathematics JO - International Journal of Discrete Mathematics SP - 15 EP - 22 PB - Science Publishing Group SN - 2578-9252 UR - https://doi.org/10.11648/j.dmath.20210601.13 AB - In mathematics, the creation and definition of new concepts is the first step in opening up a new field of research. Traditionally this step originated from intuition by a process of observation, analysis and abstraction. This article will show a general method by which most of the common notions of number theory, geometry, topology, etc., can be introduced in one and the same particular way. Therefore, we only need some of the tools of naïve set theory: a set of terms to which we apply an equivalence relation. This equivalence relation induces a partition of the terms with which we can consequently associate new concepts. By using this method’s ‘machine’ in an abstract way on arbitrary sets of terms we can create new notions at will, as we will show in this article, for instance, for bidecimal numbers of different kinds. The fact that we reverse the usual procedure of intuition before abstraction, doesn’t mean that we only create esoteric objects without any meaning. On the contrary, their abstract nature precisely provides our imagination with many possibilities for several interpretations in models in which they become useful. So, for example, we can use our bidecimal numbers to define elementary transformations on a cylinder or on a pile of tori. VL - 6 IS - 1 ER -