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In any given infinite set, there exist a certain cardinality within that set, this cardinality can be holded as a list. When you change the value of the diagonal within that list, you obtain a new number that is not in infinity, here is my problem, now that if inf + 1 = infinity, why would doing that to the diagonal be any different from simply adding or subtracting from infinity.

Perhaps the new number has a value different from the list yet if adding or subtracting from an infinite sequence gives you infinity regardless, why would it be any different doing it to a certain number within that sequence, the way I see it, the new number is not outside of infinity, yet is instead outside of the cardinality of an infinite sequence therefore isn't really greater than infinity, just different from infinity and just by cardinality, not naturally.