Okay so a couple of months ago I was watch Vi Hart's video on how .999999... is equal to 1. Some really interesting arguments that I had never heard before. Yesterday, I came across an article on Planck time, and it got me thinking about where those two ideas might work together.

So ignoring that we already know about Planck time (and the other units), could we come up with an argument/proof showing that there must be a smallest, discrete unit of time using the same methods that we can use to prove that .99999... is equal to 1, only in reverse?

Yes, I've already googled this, but I could only fight people talking about the idea, not actually doing it.