Limits are NOT approaching infinity!
Автор: Algeboy: Prof James B. Wilson
Загружено: 2025-04-15
Просмотров: 11014
Despite calculus jargon, there is no process to add infinitely nor to converge on a smooth shape from rectangles after an infinite journey. A simple taxi trip in a city can prove this to you. But that doesn't mean we can't use our imagination to help us! In fact we can show that many processes that are finite can nevertheless be done so accurately as to beat any accuracy someone challenges us to achieve. And if we have such a formula then we can simply set the margin of error to 0 and declare that as the best solution, the limit. We never go anywhere near infinity -- nothing approaches infinity -- but we do settle on robust answers that no one can improve. So in a sense we can declare victory over infinity. But the details matter and you can fool someone...including yourself!
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