Whitney extension theorem

Okay kiddo, have you ever heard of a function? It's something that tells you a number when you give it another number. For example, if you give it the number 3, it might give you 6 back.

Now, sometimes we only know what a function does on some numbers, but we want to figure out what it would do on all the other numbers too. That's where the Whitney Extension Theorem comes in.

It's like a magic trick that helps us extend the function to all the other numbers we don't know yet. We can do this by looking at the properties of the function we do know on some numbers, and using those properties to guess what the function would do on the other numbers. This way, we can get a complete picture of what the function does everywhere.

The Whitney Extension Theorem is named after a mathematician named Hassler Whitney, who figured out how to make this trick work. It's used a lot in math to solve problems when we don't have all the information we need about a function.

So, in short, the Whitney Extension Theorem helps us guess what a function would do on numbers we don't know yet, by using information about what it does on numbers we already do know.