"Mathematical Modeling" means to take mathematical
concepts and apply them to the real world. If we couldn't use
mathematics in the real world, then mathematics would be useless, and
spending billions of hours perfecting mathematics would accomplish
nothing. So, mathematicians have been cognizant of modeling mathematics
to the real world.
But infinity poses a problem for mathematical modeling.
Over the years mathematicians have found a way to
overcome this problem. Basically what they have done is to say that when
we come really close to a number, we will just call it that number,
e.g., we'll say that 1.99999999999999999 = 2. Now we can use this number
in mathematical modeling when building a bridge, or a high rise, or
constructing the flight path of rocket. Or wherever else we're using
mathematics in the real world.
But guess what? It won't solve Zeno's Paradox, because
in reality you can't go from an infinite series to a finite number.
Achilles will never catch up with the tortoise. The
javelin will never leave Achilles' hand.
To complicate the paradoxes even further there have
been those who have included the element of time in their solutions.
But it is most probable that when Zeno created his paradoxes, time
was not one of the factors that he was considering, and that would
be because time is not relevant to an object at rest. Zeno's
paradoxes are his proof that everything is at rest.
Nevertheless, since time has become interesting, due to
its complexity, which has evolved over the centuries, I have added a
short description of time.
Scientists, philosophers, and laymen alike have taken
the concept of "time" and converted it into a mysterious and
abstract idea. This has allowed the idea of "time travel," to come
into existence—mostly for use by authors and movie producers. But it
has also caused incorrect, theoretical descriptions by scientists