Hostname: page-component-8448b6f56d-mp689 Total loading time: 0 Render date: 2024-04-18T16:57:43.308Z Has data issue: false hasContentIssue false
  • English
  • Français

Redundant axioms in teaching linear algebra

Published online by Cambridge University Press:  17 October 2018

Meirav Amram ,
Miriam Dagan ,
Sagi Levi  and
Artour Mouftakhov
Meirav Amram
Affiliation:
SCE, 84 Jabotinski St., Ashdod 77245, Israel e-mail: meiravt@sce.ac.il
Miriam Dagan
Affiliation:
SCE, 56 Bialik St., Beer-Sheva 84100, Israel e-mail: dagan@sce.ac.il
Sagi Levi
Affiliation:
SCE, 84 Jabotinski St., Ashdod 77245, Israel e-mail: sagile@sce.ac.il
Artour Mouftakhov
Affiliation:
SCE, 84 Jabotinski St., Ashdod 77245, Israel e-mail: artourm@sce.ac.il
Get access Rights & Permissions [Opens in a new window]

Extract

What is an axiom? The meaning of the term ‘axiom’ varies between different fields of study. In philosophy it means a statement that is accepted without argument, while in physics the term ‘postulate’ is used and it means a theory that was verified in an experiment, and will be considered as true unless it is disproved by other experiments.

In mathematics the notion of ‘axiom’ is used in two related but distinguishable meanings: ‘logical axioms’ and ‘non-logical axioms’. Logical axioms are certain statements that are always true, and from them all tautologies of the language can be derived. Non-logical axioms are statements that are taken to be true, to serve as a premise or starting point for further reasoning and arguments.

Type
Articles
Information
The Mathematical Gazette , Volume 102 , Issue 555 , November 2018 , pp. 401 - 412
Copyright
Copyright © Mathematical Association 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Weisstein, E., Peano's Axioms, accessed April 2018 http://mathworld.wolfram.com/PeanosAxioms.html.Google Scholar
2. Shianghaw, W., A system of completely independent axioms for the sequence of natural numbers. J. Symbolic Logic Vol. 8, issue 1, (1943) pp. 41–44.Google Scholar
3. Hefferon, J., (2001) Linear algebra. Retrieved from https://www.mathematik.uni-muenchen.de/~renesse/AP09/hefferon.pdfGoogle Scholar
4. Carrell, J. B., Fundamentals of linear algebra (2005) available at https://www.math.ubc.ca/~carrell/NB.pdfGoogle Scholar
5. Axler, S., Linear algebra done right, Springer International Publishing (2015).Google Scholar
6. WIKIBOOK, Linear Algebra, accessed at https://en.wikibooks.org/wiki/Linear_AlgebraGoogle Scholar
7. Baumslag, B. & Chandler, B., Theory and problems of group theory, McGraw-Hill Book Company, New York (1968).Google Scholar
8. Lang, S., Algebra, Springer-Verlag, New York (2002)Google Scholar
9. Evas, H., Foundations and fundamental concepts in mathematics, Dover Publications, New York (1990).Google Scholar
10. Dyer, J. A., A note on redundancies in the axiom system for the real numbers, The American Mathematical Monthly, Vol. 74, no. 10, (1967) pp. 1244–1246.Google Scholar
11. Moore, G. H., Zermelo's axiom of choice: its origin, development and influence, Springer-Verlag, New York (1982).Google Scholar
12. Rutgers University, New Jersey, The Cauchy equation, accessed April 2018 at http://www.math.rutgers.edu/~useminar/cauchy.pdf.Google Scholar