Recently I watched Veritasium’s video on math’s fatal flaw. I understood some of it but one part that I particularly struggled with was Cantor’s diagonal argument. I did some research on bijection and I understand what constitutes a one to one correspondence between two sets, however what I don’t understand is how two infinite sets could possibly ever not have a one to one correspondence. Because from my limited understanding of mathematics, infinity seems to be a characteristic of a set that means its cardinality does not exist, because their is no bounds or ends to a set. I understand how the new real number is generated in Cantor’s proof, but I don’t understand how when matching the sets that one set of boundless numbers could be any more or less boundless then another. Put more colloquially, because I’m bad at phrasing this question in advanced mathematical terminology, no matter how many numbers are created using the diagonal proof, is there not another natural number that can always be matched up against it, given that the amount of natural numbers is boundless?