Semigroup with three elements

Okay little one, let's learn about something called a "semigroup with three elements."

Imagine you have three toys: a ball, a toy car and a stuffed animal. Now, let's play a game! We're going to perform an operation called "combine" on these toys.

First, we'll take the ball and combine it with the toy car. What do we get? We get another toy car! So, if we write it down like this: ball + toy car = toy car.

Next, let's combine the toy car with the stuffed animal. What do we get? We get the ball! That looks like this: toy car + stuffed animal = ball.

And finally, let's combine the ball with the stuffed animal. What do we get this time? We get the toy car! So, that looks like this: ball + stuffed animal = toy car.

We've just performed three different "operations" on our toys by combining them in different ways. And these operations follow something called the "semigroup" rule - which means if we combine any two toys in any order, we always end up with the same result.

So, a "semigroup with three elements" is just a fancy way of saying that we have three things, and we can combine any two of them in different ways, but no matter what order we combine them in, we always end up with the same result. Cool, huh?