Irrational numbers have infinite decimal expansion(their decimal part depicting fraction of a whole) and addition is a binary operation, right? Which means you need to have the knowledge of a definite measure to which you assign a symbol depicting the actual measure of a certain size. My interpretation of addition is that it depicts the next state or the measure that one can go to given a starting point, right? Now, if there's a rational number whose decimal expansion is of infinite length, then geometrically I don't have a starting point to add to or the next point in line where I might go to since I don't know that at what point should I start from. The case is even worse in the case of adding to an irrational number, why because there the decimal expansion, unlike the rational numbers basically loses predictability in its expansion, right? So I have a hard time understanding as to how can one add something to an irrational or a rational of infinite decimal expansion( I know they might have finite value but the precision to which their decimal expansions go on is not known, right) when I go by the geometric intuition of how addition takes place?