| What is a binary operator in maths? | Any operator which takes two inputs and produces an output. |
| How is a binary operator usually written? | With a symbol representing the operator placed between the two inputs. |
| What does the addition binary operator do? | Takes two numbers and produces their sum. |
| Give an example of addition. | 3 + 5 = 8 |
| What does the subtraction binary operator do? | Takes two numbers and produces their difference. |
| Give an example of subtraction. | 10 - 4 = 6 |
| What does the multiplication binary operator do? | Takes two numbers and produces their product. |
| Give an example of multiplication. | 6 \times 7 = 42 |
| What does the division binary operator produce? | The quotient of the two numbers. |
| Give an example of division. | 20 / 4 = 5 |
| What does the exponentiation binary operator do? | Takes a base number and an exponent, producing the base raised to the power of the exponent. |
| Give an example of exponentiation. | 2^3 = 8 |
| What does the modulus binary operator produce? | The remainder of the division of the two numbers. |
| Give an example of modulus. | 10 \% 3 = 1 |
| If a set S is closed under an operation, what does this mean? | The output value is always in the same set S when the inputs come from S. |
| Does the set S have to be finite for closure? | No, it just needs to be defined somehow. |
| Is the set of integers (\mathbb{Z}) closed under addition? | Yes. |
| Is the set of integers (\mathbb{Z}) closed under subtraction? | Yes. |
| Is the set of integers (\mathbb{Z}) closed under multiplication? | Yes. |
| Is the set of integers (\mathbb{Z}) closed under division? | No, because 1 / 2 is not an integer. |