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Vector spaces, fields, axioms, Zorn’s lemma.

In this article, we will see why all the axioms of a vector space are important in its definition. During a regular course, when an undergraduate student encounters the definition of vector spaces for the first time, it is natural for the student to think of some axioms as redundant and unnecessary. In this article, we shall deal with only one axiom 1 · v = v and its importance. In the article, we would first try to prove that it is redundant just as an undergraduate student would (in the first attempt), and then point out the mistake in the proof, and provide an example which will be sufficient to show the importance of the axiom.

Aniruddha V Deshmukh¹

1. S V National Institute of Technology Surat 395 007, Gujarat.

Published

6 November 2020