I get that …9999 + 1 = …000 goes to an interesting direction and …9999 + 1 = 100...000 goes to an interesting direction. And we can assume/axiom into those directions. But it can also be taken as a claim. One could explore what “2+2=5” implies but another natural reaction is also to be disinterested because one asssume things in opposition to that. So is there multiple ways to make formal or concretise the informal intuitions and does that say something interesting how addition works?
I get that …9999 + 1 = …000 goes to an interesting direction and …9999 + 1 = 100...000 goes to an interesting direction. And we can assume/axiom into those directions. But it can also be taken as a claim. One could explore what “2+2=5” implies but another natural reaction is also to be disinterested because one asssume things in opposition to that. So is there multiple ways to make formal or concretise the informal intuitions and does that say something interesting how addition works?
Some thought experiments have later some surprising use e.g. in physics. Other thought experiments don’t. It is probably difficult to predict.