Note that the first inequality is true by definition, since it follows immediately from the fact that
is irrational and hence cannot be equal to for any values of and .
Liouville's constant is an example of a Liouville number and is sometimes called "the" Liouville number or "Liouville's
number" (Wells 1986, p. 26). Mahler (1953) proved that is not a Liouville number.