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Proof by Mathematical Induction

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• Volume 1,Issue 3, Sept. 2014

Year:

2014

Type of Publication:

Article

Keywords:

Induction, Misconceptions, Proof, Complete Induction, Paradox, Mathematical Induction

Authors:

• Ashkenazi, Yehuda
• Itzkovitch, Elizabeth

Journal:

IJIRES

Volume:

1

Number:

3

Pages:

186-190

Month:

September

BibTex:

@article{86, author = "Yehuda Ashkenazi and Elizabeth Itzkovitch", abstract = "On this paper we deal with the concept of proof by mathematical induction. Mathematical induction is one of the most powerful tools for proving statements in discrete mathematics. Notwithstanding, it is studied only by students that learn the highest level of mathematics at school, even then it is taught in the most shallow way. Like in many subjects of mathematics, the student is being taught how to use the technique to prove simple propositions of certain form, without any theoretical basis to understand the validity of it. We feel that one way to achieve a better understanding of the induction can be obtained by exposing the students to a greater variety of propositions. For that matter we end this paper with some examples of varies statements proved using mathematical induction. Furthermore, it is rather odd that the concept of complete mathematical induction, which will be discussed further in this paper, and which is even a more powerful tool, is not taught at school at all. ", journal = "IJIRES", keywords = "Induction, Misconceptions, Proof, Complete Induction, Paradox, Mathematical Induction", month = "September", note = "This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. CC BY-NC-SA 4.0 Creative Commons License: https://creativecommons.org/licenses/by-nc-sa/4.0/", number = "3", pages = "186-190", title = "{P}roof by {M}athematical {I}nduction", volume = "1", year = "2014", }

Note:

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. CC BY-NC-SA 4.0 Creative Commons License: https://creativecommons.org/licenses/by-nc-sa/4.0/

Abstract:

On this paper we deal with the concept of proof by mathematical induction. Mathematical induction is one of the most powerful tools for proving statements in discrete mathematics. Notwithstanding, it is studied only by students that learn the highest level of mathematics at school, even then it is taught in the most shallow way. Like in many subjects of mathematics, the student is being taught how to use the technique to prove simple propositions of certain form, without any theoretical basis to understand the validity of it. We feel that one way to achieve a better understanding of the induction can be obtained by exposing the students to a greater variety of propositions. For that matter we end this paper with some examples of varies statements proved using mathematical induction. Furthermore, it is rather odd that the concept of complete mathematical induction, which will be discussed further in this paper, and which is even a more powerful tool, is not taught at school at all.

Full text: IJIRES_86_Final.pdf Online version [Bibtex]