Rational Numbers form Vector Space
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Theorem
Let $\Q$ be the set of rational numbers.
Then the $\Q$-module $\Q^n$ is a vector space.
It follows directly, by setting $n = 1$, that the $\Q$-module $\Q$ itself can also be regarded as a vector space.
Proof
From the definition, a vector space is a unitary module whose scalar ring is a field.
From Rational Numbers form Field, we have that $\Q$ is a field.
So the $\Q$-module $\Q^n$ fits the description.
$\blacksquare$