The concept of a function is one of the most useful abstractions in mathematics. In fact, it is an abstraction that can be further abstracted! For instance, an operator is an entity which takes functi...The concept of a function is one of the most useful abstractions in mathematics. In fact, it is an abstraction that can be further abstracted! For instance, an operator is an entity which takes functions as inputs and produces functions as outputs, thus an operator is to functions as functions themselves are to numbers. There are many operators that you have certainly encountered already – just not by that name.
I understand that most readers will find that statement obvious, but remember that we are building mathematics up from the ground - we need to be meticulous to understand the structures with which we ...I understand that most readers will find that statement obvious, but remember that we are building mathematics up from the ground - we need to be meticulous to understand the structures with which we are playing. The definition of the word inverse is, unfortunately, one of those with many meanings; however, the only meaning we need in mathematics is the following. The symbol used for the operation, which completely depends on the action being done, is called the operator.
