So I understand how to prove most of the axioms of a vector space except for axiom 10, I just do not understand how any set could fail the Scalar Identity axiom; Could anybody clarify how exactly a set could fail this as from what I know that anything times one results in itself(adsbygoogle = window.adsbygoogle || []).push({});

1u=u

1(x,y,z)=(x,y,z)

1(1,2,3) = (1,2,3)

1 (1,0,...,1) = (1,0,...,1)

I don't see how you could ever end up in a situation where you could end up with

1V≠V

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# I Axiom 10 of Vector Spaces

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