**But for universe infinity we want to imagine every event that has happened or can happen -- at any place, at any time.** In other words, we add a fourth dimension: time. Everything that has ever happened or will happen, happens somewhere, at some time. Thus each event is described by four numbers, \([w,x,y,z]\), where \(w\) is the time coordinate. We will let our coordinates be arbitrarily large, positive or negative.

So we can equate universe infinity with the set \(\mathbb{R}^4\), i.e. \(\mathbb{R}\times\mathbb{R}\times\mathbb{R}\times\mathbb{R}\).