And if you do that, you'll end up getting the Poisson distribution. And this is really interesting, because a lot of times people give you the formula for the Poisson distribution, and you can kind of just plug in the numbers and use it, but it's neat to know that it really is just the binomial distribution, and the binomial distribution really did come from kind of the common sense of flipping coins. That's where everything is coming from. But before we kind of prove that this, if we take the limit as, let me change colors, before we prove that as we take the limit as this number right here, the number of intervals approaches infinity, that this becomes the Poisson distribution, I'm going to make sure we have a couple of mathematical tools in our belt. So the first is something that you're probably reasonably familiar with by now, but I just want to make sure that the limit as x approaches infinity of 1 plus a over x to the x power is equal to e to the a x. No, sorry, is equal to e to the a. And just to prove this to you, let's make a little substitution here.