Simple binary operators

• A binary operator is simply any operator in maths which takes two inputs and produces an output.
• Usually, there’s a symbol representing the operator, placed between the two inputs.

Examples of binary operators

• Addition (+): Takes two numbers and produces their sum.
  • Example: 3 + 5 = 8
• subtraction (-): Takes two numbers and produces their difference.
  • Example: 10 - 4 = 6
• multiplication (*): Takes two numbers and produces their product.
  • Example: `6 * 7 = 42$
• riscv/division|division (/): Takes two numbers and produces their quotient (‘what they divide to make’).
  • Example: 20 / 4 = 5
• Exponentiation/powers (^ or **): Takes a base number and an exponent, producing the base raised to the power of the exponent.
  • Example: 2^3 = 8 (2 raised to the power of 3)
• modulus (%): Takes two numbers and produces the remainder of the riscv/division|division
  • Example: 10 % 3 = 1 (10 divided by 3 leaves a remainder of 1)

Sets

• The input values come from an initial set, call it S.
• IF the output value is also always in the same set S, then we say that the set is closed under that operation.
• S doesn’t have to be a finite set, just needs to be defined somehow.
  • For example, the set of integers (\mathbb{Z}) is closed under addition, subtraction, and multiplication, but not division (e.g. 1 / 2 is not an integer).