Rational Number is Computable Real Number

Theorem

Let $r \in \Q$ be a rational number.

Then, $r$ is a computable real number.

Proof

Let $\sequence {x_n}$ be defined as:

$x_n = r$

By Constant Sequence of Rational Number is Computable:

$\sequence {x_n}$ is a computable rational sequence.

By Computable Rational Sequence is Computable Real Sequence:

$\sequence {x_n}$ is a computable real sequence.

By Term of Computable Real Sequence is Computable:

$x_0 = r$ is a computable real number.

$\blacksquare$