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## Main Question or Discussion Point

I am trying to shorten and generalize the the definition of a vector space to redefine it in such a way that only four axioms are required. The axioms must hold for all vectors u, v and w are in V and all scalars c and d.

I believe the four would be:

1. u + v is in V,

2. u + 0 = u

3. u + -u = 0

4. cu is in V

I believe 1 and 2 can be used to satisfy:

u + v = v + u

(u + v) + w = u + (v + w)

and 3 and 4 can be used to satisfy:

c(u + v) = cu + cv

(c + d)u = cu + du

c(du) = (cd)u

1u = u

Not sure if I am on the right track here so any suggestions or corrections would be appreciated. Thanks to all who reply.

I believe the four would be:

1. u + v is in V,

2. u + 0 = u

3. u + -u = 0

4. cu is in V

I believe 1 and 2 can be used to satisfy:

u + v = v + u

(u + v) + w = u + (v + w)

and 3 and 4 can be used to satisfy:

c(u + v) = cu + cv

(c + d)u = cu + du

c(du) = (cd)u

1u = u

Not sure if I am on the right track here so any suggestions or corrections would be appreciated. Thanks to all who reply.