Liouville's Theorem (Number Theory)/Examples

Examples of Use of Liouville's Theorem (Number Theory)

Example: $\sqrt 2$

Applying Liouville's Theorem (Number Theory) to $\sqrt 2$:

$\size {\sqrt 2 - \dfrac p q} \ge \dfrac c {q^2} \implies 0 \lt c \le 6 - 4 \sqrt 2$

for every pair $p, q \in \Z$ with $q \ne 0$.