actually a very good exercise to understand why this argument doesn’t work. you’ll learn something about the nature of continuity and what it really means to repeat a process infinitely many times
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I remember coming up with this independently for the diagonal of a square as infinite steps
I assume it has something to do with “infinity is not a theoretical largest number, it is all numbers”
Idk tho it seems like limits are just made up to me
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the way i’d say it: infinity can be a number if you want, but “repeating a process infinitely many times” isn’t the same thing as having an answer to the question of what happens “at the end” of that process. you know what each time step n looks like for all finite n, not n = oo
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limits are a systematic procedure for extrapolating what happens “at n = oo” and it’s not at all clear that this is a sensible thing to do a priori! and sometimes it isn’t! sometimes there are multiple plausible alternatives you could argue for, sometimes there are none