1. I have more than five books.

1-2. I have over five books.
(Does it include five books?)

2. I have five or more books.
(It includes five. At least I have five books. Am I right?)

3. I have less than five books.
4. I have under five books.
( I don't have five books. I have at most four books. Is my explanation right?)

5. I have five and more books.
(Can we use this expression? At least I have seven books. Is it right?)

1. I have more than five books.

1-2. I have over five books.
(Does it include five books?) Yes, these are fine and your interpretation is right.

2. I have five or more books.
(It includes five. At least I have five books. Am I right?) Yes

3. I have fewer than five books.
4. I have under five books.
( I don't have five books. I have at most four books. Is my explanation right?) 3 is now correct; "books" is a count noun, and needs "fewer" instead of "more" (used for non-count nouns). Let me know if you need more explanation about this.And yes, your explanation is correct.

5. I have five and more books.
(Can we use this expression? At least I have seven books. Is it right?) These are a bit off. I'd say, "I have at least five books" or "I have at least seven books."

Thank you for your help.

1. I have more than five books.
1-2. I have over five books.
(Does it include five books?) Yes, these are fine and your interpretation is right.
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Doesn't it mean that I have six or more books?

"More than five books" doesn't include 'five books.' Is that right?

"more than five books" means that you have at least six! It includes the five and adds at least one more.

1. "I have more than five books" means that you have a quantity of books greater than five. This implies that the number of books you have does not include five. In other words, if you have exactly five books, this statement would not be true.

2. "I have five or more books" means that you have a minimum of five books, but you may have more than that. So yes, if you have exactly five books, this statement would still be true because "or more" includes five.

3. "I have less than five books" means that you have a quantity of books that is lower than five. This implies that you have at most four books. If you have exactly five books, this statement would not be true.

4. "I have under five books" has the same meaning as "I have less than five books." It means you have at most four books, and if you have exactly five books, this statement would not be true.

5. "I have five and more books" is not commonly used in English. A more natural way to express having a minimum of five books would be to say "I have at least five books" or "I have at least five or more books" or simply "I have at least five books." Saying "I have five and more books" might cause confusion and is not a standard expression.