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I keep seeing in textbooks and examples online that when someone proves that a set is a vector space, they only use a few of the axioms to prove it.

Is there a general guideline for when to use all of the axioms, and when you only need to use select ones to prove that a set is a vector space?

Obviously, you only need one axiom to prove that a set isn't a vector space. But for sets that are vector spaces, I'm not sure.

Finally, if you have a good example of proving that set is a vector space using all axioms, I would really appreciate it if you could post that as well :-)

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# Question about showing that a set is a vector space

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