A Note on Vector Space Axioms
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.
Volume 27 | Issue 6