Addition is the first function we learn because it's a way of counting numbers. If I have one apple and you have one apple, then if we combine our apples we would have "one and one" apples. The word "and" is used to represent counting numbers together. In mathematics, the words "function", "process", and "operation" are often used interchangably, and addition is the function of counting things together.
The act of counting happens in time, therefore there exists a before and an after. Before, you have an apple and I have an apple. After, we have an apple and another apple. We have connected together the fact that if you have an apple and I have an apple then we together have an apple and an apple.
At it's simplest form, addition is the process of "and one". The word mathematicians use to represent "and one" is increment. To increment is to "and one" or, rather, "add one". The way in which we write increment, especially in programming languages, is with the "++" symbols.
In the exercise above, we can click the "++" button to add another - to increment - the total number of "1" on the page. The Unary System, though, is a way in which we can communicate quantity with only the number "1". Unary comes from the Latin word "un" meaning "one" and "-ary" meaning "relating or belonging to." While we can use the symbol "1" to represent the number one and counting by one, we can use nearly anything to represent the number one. Counting fingers, blocks, ducks, etc. are all examples of symbols that can be used to represent the number one. We'll use the Unary Number System for the rest of this article to explain addition more broadly.
At this point, we're going to explain the notation - the way of writing - addition. Within the Unary System, the process of incrementing (++) a number is written as "+ 1". We say this as "and one", "add one", or "plus one". These are all different ways of saying the same thing - the process of adding one.
In this article we defined addition and explained it as a process of combining two things. In the next article we'll dive deeper into the Unary System and how to perform addition within it.