Another interesting relationship between powers and infinity is that on an infinite N-dimensional lattice, taking an infinitely long random walk, starting with

Another interesting relationship between powers and infinity is that on an infinite N-dimensional lattice, taking an infinitely long random walk, starting with dimension 3 you have a 34% chance to return to origin with each successive dimension reducing your chance. The graph of this probability follows a log curve. (dimensions 1 and 2 have a 100% probability of returning to origin)