Densely defined operator

Ok kiddo, let me explain what a densely defined operator is! Imagine you have a big box full of all kinds of toys. Some are really big and take up a lot of space, while others are small and don't take up much room at all. Now, imagine that each of these toys represents a special way to do something with numbers - like adding or multiplying them together.

Now, we want to use these toys to solve a problem. But the problem has some really tricky numbers in it that our toys don't know how to handle. These tricky numbers are called "outliers". They don't fit in with the rest of the numbers we normally work with.

In this situation, we want to use a special toy called a "densely defined operator". This toy is really good at handling outliers and figuring out what to do with them, even if the other toys can't.

But here's the catch - this toy only works with a certain subset of the numbers in our box. This subset is called the "domain" of the densely defined operator. It's like a special group of toys that the densely defined operator knows how to play with.

So, we use this densely defined operator toy to solve the problem, but we have to make sure we only use it with the numbers that are in its domain. Otherwise, it might not work correctly. And that's what a densely defined operator is - a special toy that's really good at handling outliers, but can only be used with a specific group of numbers.