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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
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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 

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