Every room is at the beginning of infinity. That is one of the attributes of the unbounded growth of knowledge too: we are only just scratching the surface, and shall never be doing anything else. So there is no such thing as a typical room number at Infinity Hotel. Every room number is untypically close to the beginning. The intuitive idea that there must be ‘typical’ or ‘average’ members of any set of values is false for infinite sets.
