While "takebacks" are often not granted in our daily lives, they are, in essence, the focus of much of mathematics. From undergraduatelevel algebra courses to graduatelevel economics courses, many scientists and mathematicians are just professionals at "takebacksies." We want to know why something works the way it does. In the sciences, we have the unique ability to see the reaction (or consequence) and then deconstruct, or work backwards, to figure out the action (or antecedent) that caused this event. That is, we want to find the inverse actions!

Key to Success 
While we have not officially talked about numbers, equations, or variables yet, I think it is safe to say that you have had to solve an equation for some variable (likely \(x\)) at some point in your scholastic career. Solving an equation is essentially a game of "takeback" where we "undo" a list of actions that was originally done to the variable; however, in mathematics, we say operations instead of actions.
DEFINITION  Mathematical operation and operator
In mathematics, any action that can possibly transform one or more objects into another object is called an operation. The symbol used for the operation, which completely depends on the action being done, is called the operator.
In mathematics, any action that can possibly transform one or more objects into another object is called an operation. The symbol used for the operation, which completely depends on the action being done, is called the operator.
For example, suppose somebody did something to \(k\) to turn it into \(13\). Specifically, they did the following to \(k\). \[k + 1 = 13\] The operation performed on \(k\) was addition (by \(1\)). If we really wanted to know what \(k\) was, we would perform the inverse of this operation to "undo" that addition. It just so happens that the inverse operation of addition is subtraction, but that is of no import right now.
DEFINITION  Inverse operation
The inverse operation (often just called the inverse) to any given operation in mathematics is the operation that cancels (or "undoes") the original operation.
The inverse operation (often just called the inverse) to any given operation in mathematics is the operation that cancels (or "undoes") the original operation.
Again, it is not the point of this section to have us solve equations. We will not be doing that for some time yet; however, the concept of "undoing" an action in mathematics is so important that it required just a bit of our attention.

