It takes me about forty minutes on the train to get to work in the morning. Which is a great opportunity for sleep. But today there where ladies in the seat ahead of me talking, despite it being the quite carriage.So to distract me from those inconsiderate women I counted sheep just like any other insomniac. And because I'm a an unabashed furry I anthropomised my sheep into cute bipedal sheep girls.So I sat in my seat imagining these sheep girls parading past and as they stepped in front of me I would give them an ear tag. The first numbered with zero because as well as a furry I'm a computer scientist and we always number from zero.But what was I to do with ovine friends after they received there numerical earring? Unlike other sheep counters I couldn't house them in pastures it would be inhumane and degrading. So I mentally constructed a grand hotel for them. It was simple, sheep 0 would he housed in room 0, sheep 1 in room 1, and so on. Of cause there are only as many rooms as there are room numbers because having a hotel room without a number would just be confusing.So I continued to do this for a while, but the amusement was wearing thin. So each as each girl passed I took half the time to imagine giving her her ear-ring and sending her to her room as the girl previous.Quite soon all the rooms in my hotel where filled. For each natural number there was a sheep girl and each girl was in her room. So what was I going to do with the next sheep that was looking up at me ever so cutely and bleating at me for a room and for that matter what was I going to write on her ear-tag?Given the cute ω look on her face I decided then and there that I was going to name the time compressed event ω and then named this lamb ω + 1, the sheep after ω.But where was I to house ω+1? Fortunately I knew a trick with rooms in grand hotels. I would simply move everyone into the room twice there current room number. Now we have plenty of space, so much I fired up the time compressor and filled the hotel once more.So my next sheep was ω*2+1 and I realized that these ω events could be treated like the sheep themselves and I could pull my time compression trick on them.So I spent the rest of my trip doing that, working out sequences and compressing them. When I got off at my train station I was left wondering. If I continue with this behavior is there any point that I will have more sheep then rooms to house them?