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prove that set of all integers is not a vector space

MIT 18.06 Linear Algebra, Spring 2010
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You need to specify what set the scalars are in...If the scalar set is \(\mathbb{R}\), then scalar multiplication isn't closed.
Just have to show an integer multiplied by a scalar is not an integer any more. For example, 4 multiplied by 1.2 is 4.8, which is not an integer any more. Therefore, the set of all integers is not a vetor space.

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