What is the decimal expansion of the difference of two irrational numbers $x$ and $y$ in term of the decimal expansions of $x$ and $y$.
I know that irrational number is a number which contains non-terminating and non-repeating decimal expansion. This fact makes some difficulties when calculating the difference of the decimal expansions of $x$ and $y$.
The subtlety here is that each digit may depend on an unbounded number of other digits. For example, what is the first digit after the decimal point of this difference?
$$0.247747474747747474\ldots-0.147747474747747474\ldots$$
The digits provided aren't enough to tell if the difference is $0.1000\ldots$ or $0.0999\ldots$. It depends on which term turns out to be larger, and you may have to seek arbitrarily fair to find that out. So if you were hoping for a simple arithmetical expression for each digit, you're out of luck.