OJAppSOpen Journal of Applied Sciences2165-3917Scientific Research Publishing10.4236/ojapps.2023.1311169OJAppS-129446ArticlesBiomedical&Life Sciences Chemistry&Materials Science Computer Science&Communications Engineering Physics&Mathematics Why Are There as Many Elements in the Cantor Set as There Are Real Numbers? WenbingWu1XiaojianYuan1School of Big Data, Fuzhou University of Foreign Studies and Trade, Fuzhou, China091120231311218321857, October 202326, November 2023 29, November 2023© Copyright 2014 by authors and Scientific Research Publishing Inc. 2014This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/

There are many important concepts in linear algebra, such as linear correlation and linear independence, eigenvalues and eigenvectors, and so on. The article provides a graphical explanation of how to distinguish between the concepts of linear correlation and linear independence. The conclusion points out that linear independence means that there are no two (base) vectors with the same direction in a vector graph; otherwise, it is a linear correlation.

Cantor Ternary Set Linear Independence Vector Linear AlgebraConflicts of Interest

The authors declare no conflicts of interest regarding the publication of this paper.

Cite this paper

Wu, W.B. and Yuan, X.J. (2023) Why Are There as Many Elements in the Cantor Set as There Are Real Numbers? Open Journal of Applied Sciences, 13, 2183-2185. https://doi.org/10.4236/ojapps.2023.1311169

ReferencesYang, X.J. and Baleanu, D. (2013) Local Fractional Variational Iteration Method for Fokker-Planck Equation on a Cantor Set. Acta Universitaria, 23, 3-8. https://doi.org/10.15174/au.2013.587Lyu, H.L., et al. (2022) Finding the Optimal Design of a Cantor Fractal-Based AC Electric Micromixer with Film Heating Sheet by a Three-Objective Optimization Approach. International Communications in Heat and Mass Transfer, 131, Article ID 105867. https://doi.org/10.1016/j.icheatmasstransfer.2021.105867Kigami (2010) Dirichlet Forms and Associated Heat Kernels on the Cantor Set Induced by Random Walks on Trees. Advances in Mathematics, 225, 2674-2730. https://doi.org/10.1016/j.aim.2010.04.029Collet, P., Martinez, S. and Schmitt, B. (1994) The Yorke-Pianigiani Measure and the Asymptotic Law on the Limit Cantor Set of Expanding Systems. Nonlinearity, 7, 1437. https://doi.org/10.1088/0951-7715/7/5/010Gutfraind, R., Sheintuch, M. and Avnir, D. (1990) Multifractal Scaling Analysis of Diffusion-Limited Reactions with Devil’s Staircase and Cantor Set Catalytic Structures. Chemical Physics Letters, 174, 8-12. https://doi.org/10.1016/0009-2614(90)85318-7Li, Y.S., Yang, X.D., Liu, C. Y., et al. (2011) Analysis and Investigation of a Cantor Set Fractal UWB Antenna with a Notch-Band Characteristic. Progress in Electromagnetics Research B, 33, 99-114. https://doi.org/10.2528/PIERB11053002Freiberg, U. and L?Bus, J.U. (2004) Zeros of Eigenfunctions of a Class of Generalized Second Order Differential Operators on the Cantor Set. Mathematische Nachrichten, 265, 3-14. https://doi.org/10.1002/mana.200310133