# The Properties of Addition as an Operation. (Week 5, Day 4)

• Addition is a binary operation. What that means is that it takes two numbers and does something with them to spit out a third number.
• Addition is commutative, which means that the order of the numbers doesn’t change the answer. For example 4 + 5 = 9 and 5 + 4 = 9.
• Addition is associative, which means that when adding three or more numbers together it doesn’t matter the order you perform the operation.
For example (1 + 2) + 3 = 6 and 1 + (2 + 3) = 6 so it makes sense to just write 1 + 2 + 3 = 6.
• Addition has an associated identity element, 0. It’s called an identity element because adding zero to anything is the same as letting it be itself. For example 0 + 8 = 8 + 0 = 8.
• Adding by one is the same thing as counting.

Some of you who have studied some abstract algebra may note that there is one property of addition that is usually mentioned at the same time as the identity element that is missing from my list. I am waiting until next week to go negative.