Hotel Infinity:  Part Two

The second part of Hilbert's Hotel Paradox.  What's infinity plus infinity?

Running an infinite hotel has its perks.  Even when the rooms are full you can always find space for new guests, so you proudly welcome everyone who appears at your door.  

 

When two guests arrive at once, you make room.  When ten guests arrive, you accommodate them easily.  When a crowd of hundreds appears, you welcome them all. Is there no limit to your hospitality?