In mathematics, when we say that a set of integers (whole numbers) is "closed" under a particular operation, it means that performing that operation on any two integers within the set will always result in another integer that is also within the same set.
For example:
- The set of integers is closed under addition because if you add any two integers, the result will always be an integer.
- The set of integers is closed under subtraction because if you subtract one integer from another integer, the result will also be an integer.
- The set of integers is not closed under division because if you divide one integer by another, the result may not necessarily be an integer (e.g., 5 divided by 2 is not an integer).
In essence, closure under an operation means that you can perform that operation on any two elements from the set, and the result will remain within the same set. It's an important concept in abstract algebra and mathematics in general.
Culled from AI