What are idempotent transformations?

An idempotent transformation is like pressing a button that does the same thing no matter how many times you press it.

Imagine you have a toy box, and every time you press a button on your toy robot, it goes back to its starting position, standing up straight, arms at its sides. If you press the button once, it stands up. Press it again, it still stands up. It doesn’t matter how many times you press that button, the result is always the same.

Now think of this button as an idempotent transformation. No matter how many times you apply it, the end result is just like the first time.

Another example is a door that always closes when you push it. If the door is open and you push it once, it closes. Push it again, it’s still closed. The door doesn’t care how many times you push it; it just wants to be shut.

This is like an idempotent transformation in action, applying it more than once doesn't change the final result. It's like that toy robot or that stubbornly closing door, simple, reliable, and always doing the same thing!