I tentatively believe in real numbers and differential equations because physics requires (though I also hold out hope that e.g. holographic physics or some other discrete view may enable me to go digital again). However, I don’t believe that the real numbers in physics are really made of Dedekind cuts, or any other sort of infinite set.
Shouldn’t you add probability theory to the list [physics, differential equations]? Only because probabilities are usually taken to be real numbers. I’m curious what you think of real numbers… how would you construct them? I guess it must be some way that looks a limit of finite processes operating on finite sets, right?
Shouldn’t you add probability theory to the list [physics, differential equations]? Only because probabilities are usually taken to be real numbers. I’m curious what you think of real numbers… how would you construct them? I guess it must be some way that looks a limit of finite processes operating on finite sets, right?