Something about Apologetics.

[Categories+Sheaves]

But what do Cauchy sequences or even the concept of 'real numbers', have anything at all to do with Zeno's concerns?

I think this guy explained that connection pretty well:

To begin with Zeno was simply arguing that IF the world is a continuum, then motion would not be possible.

Unless, of course, your definition of 'continuum' is not related to the mathematical one. In which case, what are you taking 'continuum' to mean?

On the contrary I would expect that since they (hypothetical aliens) are advanced enough to be capable of interstellar travel they would probably have a mathematics based on a quantum number line that is more in harmony with the physical nature of reality.

Quantum number line? Do elaborate.