According to my book, a vector space V is a set endowed with two properties:(adsbygoogle = window.adsbygoogle || []).push({});

-closure under addition

-closure under scalar multiplication

and these two properties satisfy eight axioms, one of which is:

"for all f in V there exists -f in V such that f+(-f)=0"

But then isnt this axiom redundant in describing a vector space, since we already specified that V is closed under scalar multiplication? I mean, just by closure under multiplication, we know that if f is in V, -f must be in V since -f = (-1)*f, and (-1) is a scalar..

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# Redundancy in definition of vector space?

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