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Let Z denote the set of all integers with addition defined in the usual way, and define scalar multiplication, denoted o, by: alpha o k = [[alpha]].k for all k in Z where [[alpha]] denotes the greatest integer less than or equal to alpha, for example, 2.25 o 4 = [[2.25]].4 =2..4 = 8 show that Z, together with these operations, is not a vector space. Which axioms fail to hold?

Mathematics
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Distributivity of scalar multiplication with respect to field addition (a + b)v = av + bv Compatibility of scalar multiplication with field multiplication a(bv) = (ab)v
I agree with the second answer, but why the Distributivity of scalar multiplication with respect to field addition fail to hold ?
straight out of wikipedia Distributivity of scalar multiplication with respect to field addition (a + b)v = av + bv let a=2.5 and b=3.5

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Other answers:

oh I see never mind, thx :)
let them better be a=2,5 and b=3,6
what was ur approach to finding the solutions please ? did you test for all axioms one by one ?
not really, becouse all the rest are not afected by any weird definition. Just this two
the other one also seem to work Compatibility of scalar multiplication with field multiplication a(bv) = (ab)v a=4 and b=2.5
hum ok I see, thank you mate
you have to choose two numbers where decimal part sum is bigger than 1

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