Semigroup with involution

Okay kiddo, imagine you have a lot of toys and you like to play with them. Let's call this your toy set. Now, you can have a special rule that tells you how to put your toys in order when you want to play with them. This rule is called a semigroup, and it helps you organize your toys in a certain way.

But sometimes, you might get tired of playing with some of your toys and you want to switch them up a bit. This is where the involution comes in. Involution is like a magic spell that lets you switch the places of some of your toys so you can have more fun playing with them.

So, when you have a semigroup with involution, it means you have a special way of organizing your toys, and also a magic spell that lets you switch them up. It's pretty cool, right?

In math terms, a semigroup with involution is a set of elements (your toys) and an operation (the semigroup) that tells you how to combine them, along with a special rule (the involution) that lets you switch them up in a certain way. It's like having a special set of toys that you can always play with in a certain order, but also have the option to change them up when you want to.