Every number $x \in \mathbb{R}$ has an associated irrationality measure $\mu(x)$. Let $\mathbb{A}$ be the algebraic numbers and let $x_\mathbb{Q} \in \mathbb{Q}, x_{\mathbb{A}\setminus\mathbb{Q}} \in \mathbb{A}\setminus\mathbb{Q}, x_T \in \mathbb{R}\setminus\mathbb{A}$, and $x_L$ a Liouville number. Then
$\mu(x_\mathbb{Q}) = 1$,
$\mu(x_{\mathbb{A}\setminus\mathbb{Q}}) = 2$,
$\mu(x_T) \geq 2$, and
$\mu(x_L) = \infty$.
So any number $x_T$ with $\mu(x_T) > 2$, due to the definition of the irrationality measure, can be better approximated by rationals than any algebraic number (because $\mu(x_{\mathbb{A}\setminus\mathbb{Q}}) = 2$, but $\mu(x_T) > 2$ is better).
Now I don't understand this sentence on Wikipedia ( https://en.wikipedia.org/wiki/Liouville_number ):
They [Liouville numbers] are precisely those transcendental numbers that can be more closely approximated by rational numbers than any algebraic irrational number.
But what about those numbers with $2 < \mu(x_T) < \infty$? They are not Liouville numbers, but still they can be better approximated by rationals (i.e. they have larger irrationality measure) than any algebraic number.