Rational Number is Algebraic
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Let $r \in \Q$ be a rational number.
Then $r$ is also an algebraic number.
Let $r$ be expressed in the form:
- $r = \dfrac p q$
Consider the linear polynomial in $x$:
- $q x - p = 0$
which has the solution:
- $x = \dfrac p q$
Hence the result, by definition of algebraic number.