Countable California

The Countable California Hotel has an countably infinite number of rooms, which is handy, because an infinite number of guests showed up one night. The clerk on duty put the first guest in room 1, the second in room 2, and so on.

When the manager showed up the next morning, he discovered the clerk's bad mistake. He knew that an infinite number of new guests was showing up tonight, but that since it was the Countable California, some of the guests might check out, but none of them would ever leave.

"The bellhops will be busy moving luggage today," he said.

How did he solve his problem?

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