Something about Apologetics.

[Abracadabra]

The calculus limit has nothing to do with Zeno's objections concerning the idea of being able to actually complete an infinite number of tasks. They simply have nothing to do with each other at all.

When a mathematician asserts that the real numbers are isomorphic to the ring of cauchy sequences in the rational numbers modulo said sequences that converge to zero, how does this fail to assert that we can treat the product of an infinite number of tasks as a completed object?

It doesn't.

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

The very notion of 'real numbers' is a man-made mathematical concept that has nothing at all to do with what Zeno was talking about.

You need to realize that the very notion of a "number line" that itself is assumed to be a "continuum" is the product of the imagination of mathematicians who themselves have arbitrarily assumed that reality can be correctly described as a continuum. So they are already assuming a continuum by their own artificial definitions.

I personally don't even agree with human mathematics in the details. Much of it is nothing but man-made whims.

In fact, I personally believe that if aliens came here from another planet they may very well have a system of mathematics that is not based on the idea of a 'continuous number line' like we do.

On the contrary I would expect that since they 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.

I personally believe that humans will eventually move beyond their current man-made mathematical formalism and move to a mathematics that's more closely aligned with physical reality.

I also suspect that this will most likely happen fairly soon. Probably within the next century or so. Although mathematicians certainly aren't moving in that direction at the present time.