The set of integers is closed under the operations of addition, subtraction, and multiplication.
Here’s why:
- Addition: When you add any two integers together, the result is always an integer. For example, if you take -3 and 5, their sum is 2, which is also an integer.
- Subtraction: Similar to addition, if you subtract one integer from another, the result is still an integer. For instance, subtracting 5 from -3 gives you -8, an integer.
- Multiplication: When you multiply two integers, their product is also an integer. For example, multiplying -3 by 4 results in -12, still an integer.
However, the set of integers is not closed under division. For example, dividing 1 by 2 gives you 0.5, which is not an integer.
In summary, the integers form a closed set under addition, subtraction, and multiplication, but not under division.