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Vectors: proof (uni level)

Q1. Prove (without using coords) that u+0=u for each vector u. [hint: let AB represent u, and then represent 0 appropriately to be able to apply the triangle rule.

thanks in advance
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nuodai
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What are the assumptions being made here? It seems like a silly question because under most constructions 0 is defined to be the vector such that for any vector u in the vector space, u + 0 = u.
(edited 13 years ago)
nuodai
What are the assumptions being made here? It seems like a silly question because under most constructions 0 is defined to be the vector such that for any vector u in the vector space, u + 0 = u.


Is shown to satisfy certainly not defined.

Question in the thread: What do you want a vector to do? So what would a vector that left all points where they lie do?

Under the assumption additive inverses are present - that is given some vector v there is a vector u that takes all points after translated by v and takes them back as they were it should be easy to show.

This leaves alot to be desired as the majority of the case we go - there exists a vector 0 for all vectors v 0 + v = v (= v + 0) followed by saying additive inverses exist; for all v there exists u u + v = v + u = 0.

Though the emphasis seems to be getting some geometric exploration and grounding as to how vector spaces can be used geometrically so the previous approach seems all fine for that intention.

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