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In a thread in this forum relating to a problem on Subspaces I read that as long as a Vector SubSpace is closed under addition and multiplication we always have the zero vector. I can see that we can always get the zero vector but do we not have to define a zero vector first as given in the Vector Space axioms or can we make it by manipulation IE multiplying a vector by minus one and adding this to the original vector. This seems somehow contrived to me so is it OK to get the zero vector in this manner or does it first need to exist by definition.If we can always get it by manipulation in this way it seems unnecessary to require it by definition.

( I know that we are allowed the Zero Vector alone to be a vector space and so cannot get it any other way in this case )

Thanks for any clarification on this query as I am still learning and want to understand fully.

Matheinste

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# Zero Vector

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