Addition is the joining of two sets to form a new set.
When we write 4 + 3 = 7 we are representing that the result of joining a set of four to a set of three is a set of seven objects.
Addition is a binary operation in that we can only join two sets at once. When we work with the set of counting numbers {1, 2, 3…} the answer is greater than either of the sets being joined.
This is not always true when we add integers which include zero and negative numbers.
Subtraction is the separation of a subset from a set, sometimes described as taking away a part from the whole.
When we write 7 – 3 = 4 we are representing the result of taking a subset of three from a set of seven objects, leaving a subset of four objects.
Addition and subtraction are also applied when comparing sets.
We can represent the difference between a set of three and a set of seven using either addition, 3 + ? = 7, or subtraction, 7 – 3 = ?
