This may sound impossible, but we are very familiar with the concept of something being finite but unbounded when considering a two-dimensional surface existing in three-dimensional space. Think, for instance, of the surface of the Earth. It is definitely finite: travel around its equator and you will come back to your starting point in around 40,000 kilometres (25,000 miles). You can reach any point from any other after travelling a finite distance that is no more than half this distance. But the Earth’s surface has no boundary, no ending. You can travel around it for ever without coming to the edge.