>>12883518>Even if we where not able to give a definition of what an integer is as long as our human intuition points to the same abstract thing and everybody treats it with the properties that the abstract thing has, even if you are not able to give a explicit definition, then whats the fucking problem yo cunt retard?I agree with you. After all, definitions have to stop somewhere, you can't just keep on asking to define things ad infinum. Usually the concepts become clear or sufficiently clear after a few levels of definitions, as is the case with rationals and integers. I'm sure you could act in bad faith and keep asking me to define things, define a string, define a stroke, etc. In the end I would be out of words and could not convey the idea any clearer.
However, there is a difference. With rationals and integers, I genuinely feel I understand what is meant by them, and I think so does everyone who hasn't failed middle school arithmetic, if they're acting in good faith.
But with reals, I genuinely have no idea what a general real is. And this is not a purely abstract, philosophical declaration, but a practical one. If you tell me to build a system that takes the type of X, I would be able to do it for rationals, integers but not reals. Whatever system I could attempt to come up with for the "reals", it would always be missing some reals, there would always "be" reals that could not fit into such a scheme.
So I view the concept of reals just like mathematicians viewed complex numbers in the time of cardano. A kind of vague appeal to some intuitive ideas, in some cases easy to manipulate objets, but without any actual definition of proper construction, which only came later.
