A brief description of the paradox taken from Wikipedia:
Suppose Sam wants to catch a stationary bus. Before he can get there, he must get halfway there. Before he can get halfway there, he must get a quarter of the way there. Before traveling a quarter, he must travel one-eighth; before an eighth, one-sixteenth; and so on.
This description requires one to complete an infinite number of tasks, which Zeno maintains is an impossibility. This sequence also presents a second problem in that it contains no first distance to run, for any possible (finite) first distance could be divided in half, and hence would not be first after all. Hence, the trip cannot even begin.
The paradoxical conclusion then would be that travel over any finite
distance can neither be completed nor begun, and so all motion must be
an illusion.
How can this be disproved using math, as obviously we can all move a walk from one place to another?
Best Answer
It can't. It's not a mathematical statement, it's a statement about the nature of physical space.
At least for the first problem, the obvious mathematical answer is that the "total distance" is finite, because it's the infinite sum $\sum 2^{-n}$, which converges. But the whole point of the paradox is that it's making a statement about the physical world. It's philosophically difficult to say whether or not the above infinite series argument can really be applied to physical space. In particular, is it even meaningful to subdivide a physical length indefinitely? Are physical lines fundamentally continuous or discrete? Do any of these questions really mean anything?
No matter how far you postpone it, at some point you're going to have to cross the bridge from the mathematical model into the real world, and that will always be a philosophical problem, not a mathematical one.