Cantor Set from a Nonstandard Viewpoint

Authors

Sebar H. Jumha, Department of Mathematics, College of Science, Salahaddin University-Erbil, Erbil (Hawler), Kurdistan Region, Iraq
Ibrahim O. Hamad, Department of Mathematics, College of Science, Salahaddin University-Erbil, Erbil (Hawler), Kurdistan Region, IraqFollow
Ala O. Hassan, Department of Mathematics, College of Science, Salahaddin University-Erbil, Erbil (Hawler), Kurdistan Region, Iraq

Corresponding Author

Ibrahim O. Hamad

Authors ORCID

0000-0002-3994-1866

Document Type

Original Article

Abstract

This paper proposes a fresh perspective for visualizing the Cantor set and explores its shading characteristics through the utilization of nonstandard tools and techniques. Our investigation reveals that the measure of the Cantor set is infinitely close to zero but not identically zero, and we validate the properties of the Cantor set using an assortment of nonstandard methodologies. These findings have far-reaching implications for enhancing our understanding of mathematical approximations and exact measurements. Furthermore, we correlate our nonstandard perspective outcomes regarding the Cantor set with some specific applied models.

Keywords

nonstandard, Cantor set; infinitely close; measure zero; uncountable set.

How to Cite This Article

Jumha, Sebar H.; Hamad, Ibrahim O.; and Hassan, Ala O. (2024) "Cantor Set from a Nonstandard Viewpoint," Polytechnic Journal: Vol. 14: Iss. 1, Article 12.
DOI: https://doi.org/10.59341/2707-7799.1830