Yes, that is one example of many arbitrary choices in infinite systems. In practice that means that you give up the ability to communicate to anyone else which system you’re working with, unless you also have a channel with which to communicate an infinite amount of information to them.
Well, that’s trivially simulatable, since I can generate an infinitely large communication channel, so that’s not a constraint.
Well, that’s trivially simulatable, since I can generate an infinitely large communication channel, so that’s not a constraint.