So wait did anyone ever fix the whole "to cross a distance I must cross half the distance etc" all distance contain an infinite sum thing? Is the answer just that infinite sums can have finite results?
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in the mathematical model, yes, infinite sums (over either distance or time) can have finite results. in “the real world” (slightly less idealized model) it’s not at all clear that it’s possible ro infinitely subdivide space or time, or perform infinitely many actions
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a thing that i think mathematicians and physicists don’t do a good job of conveying is that most of our use of large infinite objects like the real numbers is a matter of convenience. the infinite is a convenient approximation of the merely unimaginably large finite
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at infinity all the error terms disappear so you only have to work with the asymptotic behavior. when we do something like model heat diffusion with the heat equation we are *approximating* the behavior of ~avogadro’s # of particles by the solution to a differential equation