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It is said that an infinite can't be traversed.  It actually depends on what you have an infinite number of.  An infinite number of physical things can't be traversed.  An infinite number of abstractions (like whole numbers) also can't be traversed - even abstractly traversed.  Any unit multiplied infinitely can't be traversed.  But Zeno's alleged paradox refers to an infinite number of divisions between two points.  Multiples and divisions are opposite concepts.  What is true of one is not necessarily true of the other.  The distance between any two points can be traversed.  Even opposite ends of the universe can be traversed theoretically.  The distance between any two points can also be divided infinitely (assuming space is infinitely divisible).  And these divisions are irrelevant to the fact that the distance between any two points can be traversed.  Every motion is a traversion of an infinite number of spatial divisions.

It's as simple as this:
An infinite of multiples can't be traversed.
An infinite of divisions is traversed with every motion.

All that stuff about having to get half way there first is irrelevant.