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buckaroobill
04-17-2007, 02:02 PM
This problem was confusing me, so any help would be appreciated!

Here is a vector candidate. The set is R, and we define scalar multiplication by ax = a * x (usual scalar multiplication) and vector addition by x\oplusy = max(x, y).

For each of the following three vector space axioms, either verify the axiom or show that it does not hold.

a) a(x+y) = ax + ay
b) There exists an element 0 such that for any x in the proposed vector space, x + 0 = x.
c) x+y = y+x