infinite number of rooms are all occupied by a person.. then a person shows up. There is one to one ratio here... of all rooms are occupied by a person.. infinite rooms.. infinite people.. if the infinity of people are all ready in the infinity of rooms..
Then who is showing up? Everyone is already in the rooms.. So no need to worry about moving anyone.
If we change it to be numbers it still doesn't work.. If we have an infinite amount of slots.. and in each slot is a number.. and all slots are full.. how can we make room for another number..
If you say that oh well there were only even numbers in the slots.. well then what you told me isn't true.. all slots aren't full with numbers.. only even numbers..
I understand what the paradox is trying to explain about sets.. but to me it just falls apart as a metaphor.