Is it true that a worn-out book carries exactly the same amount of information as a new one?

Right. Because the amount of information in both books is unchanged, both books contain the same set of letters, words, sentences, they are absolutely identical.

Remember: The process of learning a person lasts a lifetime. The value of the same knowledge for different people may be different, it is determined by their individual characteristics and needs. Therefore, knowledge is always needed at any age and position.