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.
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.