Let Z denote the set of all integers with addition defined in the usual way, and define
Chapter 3, Problem 14(choose chapter or problem)
Let Z denote the set of all integers with addition defined in the usual way, and define scalar multiplication, denoted , by k = [[]] k for all k Z where [[]] denotes the greatest integer less than or equal to . For example, 2.25 4 = [[2.25]] 4 = 2 4 = 8 Show that Z, together with these operations, is not a vector space. Which axioms fail to hold? 1
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