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I've some trouble understanding (or maybe accepting) Cantor's diagonal argument. When I was young I had no trouble accepting it and it seemed perfectly logical, but after a long hiatus and returning to my original interests, I seem less than convinced (must be some age-related or brain decay issue :-)

Now let's say I have the set of all positive integers. This set is clearly countable/enuimerable, so I can place all its members in a sequential list. What stops me from applying the diagonal argument to this list, and getting a positive integer that does not belong to the set, which by definition contains all positive integer? what gives?