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What is the importance of last axiom of vector space. Axiom is $1u=u$.

Shaun
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Zahid Latif
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    See here for a discussion. – Dietrich Burde Feb 16 '15 at 10:06
  • I'm going to close this as a duplicate to the linked question, because asking "what do we need an axiom for" is essentially asking "how would the theory be different without the axiom", and that can be exemplified by models where only that axiom fails. But anyone wishing to add to this question, feel free to answer at the duplicate. – Marc van Leeuwen Feb 16 '15 at 10:27

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In each operation, you need a neutral element. For $+$ it's $\vec 0$ and for the multiplication by a scalar, by this axiom, it's $1$.

Surb
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