I struggle to understand why disjunctive numbers are necessarily transcendental.
A rich number (or disjunctive number) is a real number whose expansion, in a given base $b$ is a disjunctive sequence over the alphabet $\{0, ..., b − 1\}$, i.e. it contains any finite sequence of digits, at least once, expressible in that base (in other words, it contains the whole “universe” of finite integers, at least once, expressible in base $b$)
I read this in the OEIS Wiki : "[...] Thus, disjunctive numbers (in base $b$) contain, at least once, all $n$-digits approximations (ignoring the fractional point) for all real numbers (including at least a second occurrence of all $n$-digits approximations of itself or not?), which means that disjunctive numbers are transcendental numbers and constitute an uncountable subset of the real numbers."
But I don't understand the argument.
Why the fact that containing at least once all n-digits approximations of every real numbers means that the number cannot be the root of a non-zero polynomial of finite degree with rational coefficients ?
(I apologize for the potential english mistakes I'm still learning it)