Thinking About Infinity

In an actually infinite library, the number of books with green spines will be equal to the number of books with black spines. Yet the number of books with green spines will be equal to the total number of books in the library. What do you think happens to the total number of books in this library when I borrow a book, and what happens to the total number of books in the library when I return the book?

Can you give any examples of infinite things? Anything of infinite size, length, number, contents?

A series of numbers is only potentially infinite. If the universe had no beginning it would be actually infinite. Is this possible?

Imagine that you go into an actually infinite library to borrow a book that you have always wanted to read. The librarian tells you it is on shelf K. Do you think that it is possible for you to reach the book that you want to borrow?
Would you know that you were in an infinite library?

∞

Imagine you came to stay in a hotel with an infinite number of rooms. When you arrive you are told all of the rooms are full. You ask the receptionist to ask everyone in the hotel to move up one number of room and then go and check the room number one.
He does so, and on his return he is pleased to tell you that although no-one has checked out of the hotel it turns out room number one is now empty!

Which of the symbols behind is the best symbol for actual infinity? Which is the best for potential infinity? Give some reasons for your answers.
Does imagining time as a circle help us at all in dealing with the concept of infinity?