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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you actually don’t need a background in real analysis or topology even, although it would help you go deeper; the basic conceptual mistake can be explained more simply
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although having understood the basic conceptual mistake, if you did take a calculus class you may subsequently wonder why the same objection doesn’t apply to the definition of an integral in terms of riemann sums. this is a good question and surprisingly subtle imo!
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is the answer that the resulting circle is infinitely wrinkly with the extra length
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i would say it more simply - there just is no “resulting” shape at all, circle or otherwise
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