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Level 8

Axioms (Rules) for Vector Space as a Nonempty Set

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Closure Properties
if u is in V and v is in V, then u+v is in V
Existence Properties
There is such a zero vector in V such that u+0=u.
Distributive Properties
c(u+v)= cu+cv
Associative Properties
(u+v)+w= u+(v+w)
1u= u
Multiplication scalar 1