Really good article. > You don’t have to explain how you’re choosing elements. We’ll just assume you can make it work somehow. Very interesting remark. The wa

Really good article. > You don’t have to explain how you’re choosing elements. We’ll just assume you can make it work somehow. Very interesting remark. The way I think about it now after reading your article is: If you prove something with the axiom of choice, all you need to do is provide an ordering to get practical results from it. If you fail to do so, oh well. That being said, I don't think you need R (the reals) for practical applications, countably infinite sets like IQ (intervals over Q) are enough and the well-ordering rule doesn't seem paradoxical anymore (countably infinite sets can be ordered as there is a bijection to N). Example: Pi can be approximated arbitrarily close with a lower and upper bound on Q. The functions used to derive the lower and upper bound with arbitrary precision (also a number in Q) are Pi in this sense