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**Unformatted text preview: **every step, be sure to cite any properties of (continuous) functions that you are using. (4) 3.1.10. Prove that this set is not a vector space by explicitly providing a counterexample which demonstrates that at least one of the axioms fails to hold. (5) 3.1.7. Prove using the vector space axioms that any vector which satisﬁes the deﬁning property of the zero vector must actually be the zero vector itself. At every step, be sure to cite which axiom you are using. (6) 3.1.8. Begin with one side of this equality, and work to the other side of the equality using only the vector space axioms. At every step, be sure to cite which axiom you are using. (7) 3.1.9a. Begin with one side of this equality, and work to the other side of the equality using only the vector space axioms. At every step, be sure to cite which axiom you are using. * Two envelopes will be outside of my oﬃce door if you turn the problem set in after 6PM. 1...

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