Only, This Is Flawed Too

It’s eminently possible that the time it takes to finish each step will still go down: half the original time, a third of the original time, etc, but that the total journey will take an infinite amount of time.

You can check this for yourself by trying to find what the series [½ + ⅓ + ¼ + ⅕ ++ …] sums to. As it turns out, the limit does not exist: this is a diverging series.

Pure mathematics alone cannot provide a satisfactory solution to the paradox, as it isn’t simply about dividing a finite thing up into an infinite number of parts, but rather about the inherently physical concept of a rate