## On the Subject of Functional Mapping

Let me show you a map to the world, where the world is a function.

On the module is a function diagram for a function f(x) being mapped, a stage number, and 2 buttons.

The function is being mapped in the form f: A -> B, where A is the domain (left side of the module) and B is the codomain (Right side of the module). The arrows then show which "preimage" or domain element gets mapped to an "image" or codomain element.

To solve the module, you will have to press the correct button on top that is being displayed. There is a configuration for the number of stages you can have. For an understanding on what Surjection and Bijection is, look down below.

### How to solve the module:

##### Surjection:

A Surjection is a mapped function where for every element on the left side of the module, there is a element on the right side, and f(left side element) = right side element (or for math sakes, for every element a in A, there is an element b in B with f(a) = b). Also, the mapping can be many to one, meaning that a codomain element can have multiple domain elements mapped "onto" it.

##### Bijection:

A Bijection is a mapped function where every element is going to exactly ONE element and it surjective.