Good point. But if you instead take the line itself as primitive like Euclid did, you still need two points on it to define the line you mean, and while you have the starting points, I’m not sure where your second point is, since you’re not assuming there is a point where the two lines cross. How, exactly, do you draw the lines in that case?
Side note: identifying the algebraic equation d=rt with a line requires a coordinate system. What coordinate system are you using? What set of numbers are you drawing the allowed coordinate values from? Do those numbers form a field in which all the basic arithmetic operations are well defined?
The point I’m trying to get at is: Zeno’s paradox is only a paradox because 1) he didn’t accept the idea of a completed infinite set, and 2) many of his ideas about math and logic were ungrounded and underspecified. It’s very hard to still think of these as paradoxical once you’ve seen how to build up the foundations of math from set theory (for which the assumptions are very simple) including geometry, arithmetic, algebra, and so on.
Good point. But if you instead take the line itself as primitive like Euclid did, you still need two points on it to define the line you mean, and while you have the starting points, I’m not sure where your second point is, since you’re not assuming there is a point where the two lines cross. How, exactly, do you draw the lines in that case?
Side note: identifying the algebraic equation d=rt with a line requires a coordinate system. What coordinate system are you using? What set of numbers are you drawing the allowed coordinate values from? Do those numbers form a field in which all the basic arithmetic operations are well defined?
The point I’m trying to get at is: Zeno’s paradox is only a paradox because 1) he didn’t accept the idea of a completed infinite set, and 2) many of his ideas about math and logic were ungrounded and underspecified. It’s very hard to still think of these as paradoxical once you’ve seen how to build up the foundations of math from set theory (for which the assumptions are very simple) including geometry, arithmetic, algebra, and so on.