Cantor’s diagonal argument is not “I can find +1, and n+1 is more than n”, which indeed would be wrong. It is “if you believe that you have a countable set that already contains all of them, I can still find +1 it does not contain”. The problem is not that +1 is more, but that there is a contradiction between the assumption that you have the things enumerated, and the fact that you have not—because there is at least one (but probably much more) item outside the enumeration.
I am sorry, this is getting complicated and my free time budget is short these days, so… I’m “tapping out”.
Cantor’s diagonal argument is not “I can find +1, and n+1 is more than n”, which indeed would be wrong. It is “if you believe that you have a countable set that already contains all of them, I can still find +1 it does not contain”. The problem is not that +1 is more, but that there is a contradiction between the assumption that you have the things enumerated, and the fact that you have not—because there is at least one (but probably much more) item outside the enumeration.
I am sorry, this is getting complicated and my free time budget is short these days, so… I’m “tapping out”.