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
Yes but the point was that it couldn’t be proved using the construction that he defined. You can prove it easily with a different construction, such as defining the hand moves 1 meter per second and the object is 1 meter away, therefore takes 1 second to reach. But they couldn’t yet deal with this alternate definition that still followed all the existing mathematical rules they had at the time. A finite distance could be divided in half, creating two smaller finite distances, but they had no concept of infinity or convergence, so they had no tools to deal with a recursive division.
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
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Yes but the point was that it couldn’t be proved using the construction that he defined. You can prove it easily with a different construction, such as defining the hand moves 1 meter per second and the object is 1 meter away, therefore takes 1 second to reach. But they couldn’t yet deal with this alternate definition that still followed all the existing mathematical rules they had at the time. A finite distance could be divided in half, creating two smaller finite distances, but they had no concept of infinity or convergence, so they had no tools to deal with a recursive division.