# Argument for the Smallest Division of Time? [duplicate]

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.

• I always thought there were an infinite number of time measuring units (or close to it). When you think about it, we can get to even smaller increments than whats already out there now, but trying to measure them in practice and do all the other stuff involved with it could get a bit tedious and would take some time... – Harry David Oct 27 '14 at 9:32
• possible duplicate of Is time continuous? – Carl Witthoft Oct 27 '14 at 11:44
• Only if you can define what happens "between" clicks of quantized time, which IMHO you can't. The only thing you can do is find a Planck-ish time slice such that no observable change happens (in any system) in less elapsed time. – Carl Witthoft Oct 27 '14 at 12:39