# Is $0.112123123412345123456\dots$ algebraic or transcendental?

Let $$x=0.112123123412345123456\dots$$
Since the decimal expansion of $$x$$ is non-terminating and non-repeating, clearly $$x$$ is an irrational number.

Can it be shown whether $$x$$ is algebraic or transcendental over $$\mathbb{Q}$$ ? I think $$x$$ is transcendental over $$\mathbb{Q}$$. But I don’t know how to formally prove it. Could anyone give me some help ? Any hints/ideas are much appreciated. Thanks in advance for any replies.

My Number:

$$x=0.\underbrace{1}_{1^{st}\text{ block}}\overbrace{12}^{2^{nd}\text{ block}}\underbrace{123}_{3^{rd}\text{ block}}\overbrace{1234}^{4^{th}\text{ block}}\dots \underbrace{12\dots n}_{n^{th}\text{ block}}\dots$$
where $$n^{th}$$ block is the first $$n$$ positive integers for each $$n\in \mathbb{Z}^+$$.

(That is the 10th block of $$x$$ is $$12345678910$$; The 11th block is $$1234567891011$$; … )