Zeno's Dichotomy Paradox

    There is a famous paradox originating from ancient Greece known as Zeno's Dichotomy Paradox after the Greek Philospher Zeno of Elea. Essentially the argument is as follows. In order to travel any distant (say 1 metre) once must first travel 1/2 metre, however, before travelling 1/2 metre one must travel 1/4 of a metre and so on. The argument concludes that this represents an infinite number of tasks and so cannot be completed in a finite amount of time.
    Now, clearly this argument is wrong as we can move and so we must ask what exactly is wrong with the argument? The paradox is most often approached in terms of the convergence of infinite sums. This approach has its merits but in some respects dodges the question asked so instead I will approach it differently.
    I contend that one of the initial assumptions is wrong. I say that distance cannot be infinitely subdivided into smaller and smaller pieces. This contention is, however, at odds with the real number system we use for measuring things such as distance. I approach this question using the notion of the Planck length. The Planck length (or distance) is a term stemming from Quantum mechanics (see the wiki page). I don't pretend that the argument I present is in any way tight in terms of formal logic or physics but I propose a solution based on the idea that the Planck length is a possible basic unit of distance meaning that any length (such as a metre) is a multiple of a large but ultimately finite number of Planck lengths. This would mean that the number of tasks is not infinite and so motion is not an impossibility. I leave the argument as it stands -just the bare bones- and leave it to any readers to flesh it out.