I hated this “paradox” from the first time I encountered it sometime in grade school. I didn’t have the mathematical language for it at the time, but I distinctly remember arguing that as the number of intervals increases, the time to move one subdivision decreases, so there is no paradox at all. Basically, it doesn’t take much creativity to have a qualitative feeling for the concept of a convergent infinite series (which is what this is), but the teacher insisted it was a paradox, I couldn’t prove them wrong, and it frustrated the crap out of me.
One of the definitions of paradox is a thing you know for sure is wrong, but can’t disprove it. Zeno knew Acchiles would reach the turtle in his paradox somehow, but without calculus (or algebra, for that matter) he couldn’t explain it
I hated this “paradox” from the first time I encountered it sometime in grade school. I didn’t have the mathematical language for it at the time, but I distinctly remember arguing that as the number of intervals increases, the time to move one subdivision decreases, so there is no paradox at all. Basically, it doesn’t take much creativity to have a qualitative feeling for the concept of a convergent infinite series (which is what this is), but the teacher insisted it was a paradox, I couldn’t prove them wrong, and it frustrated the crap out of me.
One of the definitions of paradox is a thing you know for sure is wrong, but can’t disprove it. Zeno knew Acchiles would reach the turtle in his paradox somehow, but without calculus (or algebra, for that matter) he couldn’t explain it