Suppose that hilbert’s grand hotel is fully occupied on the day the hotel expands to a second building which also contains a countably infinite number of rooms. show that the current guests can be spread out to fill every room of the two buildings of the hotel.

glass wants to live in a world of super heroes and villains. he have lived all his life trying to be responsible for the creating the origin story of a super hero; he schemed and caused many incidents (many of them fatal) hoping that someday someone with superpowers would show up and save the day.

he knew himself very much. he saw himself as a villain of a real-life super hero story. he was aware of his strengths (more than smart enough for being manipulative and scheming) and weaknesses (having fragile bones and having to rely on his mind to succeed).