https://maximummathematics.com/books/foundational-mathematics/set-theory/set-partitions/index.htmlWhen working with a set of related objects, we may want to split that set up into smaller, more manageable sets. For example, we may want to split up the integers based on parity: even integers, and odd integers. When dealing with the real numbers, we may want to split them up into three separate sets: the positive real numbers, the negative real numbers, and the number $0$. One more example may be the positive rational numbers, where we split them up based on how big they are — we may have all of the positive rational numbers less than $1$ in one set, and all of the positive rational numbers greater than or equal to $1$ in the other set.Hugoen-US