Continued fraction

Let $x \in \mathbb{R}$. Then $x$ has a continued fraction expansion, notated $x=[a_0;a_1,a_2,\ldots]$ if $x$ can be represented as $$x = a_0 + \dfrac{1}{a_1+\dfrac{1}{a_2+\dfrac{1}{a_3+\dfrac{1}{\ddots}}}},$$ where each $a_i$ is an integer.