https://medium.com/question-time/ask-dr-silverman-8-infinity-behind-every-real-infinite-is-a-silver-lining-infinite-ca48e718070

Early puzzles about the infinite might have begun with the ancient Greek philosopher Zeno. One version of his paradox of the infinite is this: “An arrow goes halfway to its target. It then goes another halfway, and repeats the processan infinite number of times. Therefore, it can never reach its target.” But, of course, the arrow does reach its target. Zeno lived long beforethe concept of a limit (the basis of calculus) was discovered independently by Newton and Leibniz. They showed that infinite sums can converge to a finite limit. In Zeno’s case, we can begin with one half, then add half of that (one fourth) and keep adding halves. This infinite series has the limit 1, which is the Zeno target.

Early puzzles about the infinite might have begun with the ancient Greek philosopher Zeno. One version of his paradox of the infinite is this: “An arrow goes halfway to its target. It then goes another halfway, and repeats the processan infinite number of times. Therefore, it can never reach its target.” But, of course, the arrow does reach its target. Zeno lived long beforethe concept of a limit (the basis of calculus) was discovered independently by Newton and Leibniz. They showed that infinite sums can converge to a finite limit. In Zeno’s case, we can begin with one half, then add half of that (one fourth) and keep adding halves. This infinite series has the limit 1, which is the Zeno target.