Hello everyone!
I said a few weeks back that I'd define the real numbers for you. That's what I'd like to do today. Last time I mentioned the real numbers, I said we could think of them as infinite decimals. That is a useful way to think of them for a lot of purposes, but it doesn't really give us a way to work with them rigorously.
To start with, let's take a few big steps back. There are a lot of real numbers (uncountably many, in fact), so let's work with something simpler. Say for the moment all we have is the number 
. We could actually go further back than that, but it's not easy to rigorously define , so for now, that's a good start.
by 