I believe that potential infinity (i.e. the idea of intervals becoming ever smaller and smaller) will be sufficient to deal with the "real world". But the infin

I believe that potential infinity (i.e. the idea of intervals becoming ever smaller and smaller) will be sufficient to deal with the "real world". But the infinities described in the article are of a different kind. I don't think there will ever be a situation like: "According to the axiom of choice, this photon should go to the left, but according to the axiom of something else, this photon should go to the right." Or: "If there is such a cardinal X that mumbo-jumbo(X) is true, then the photon should go to the left, otherwise it should go to the right." Therefore, this part of math is just playing with words. An interesting game, especially if you can get paid for it, and it can provide indirect benefits such as greater insight into how to correctly play with words, but ultimately just a game with no correspondence to the "real world".