Trivial semigroup

Imagine you have a group of friends who like to play games together. Now, let's say they want to play a game where they combine two actions. For example, they can walk and talk at the same time.

A semigroup is like this group of friends. It's a collection of actions that you can combine together to get a new action. But a trivial semigroup is kind of boring.

In our group of friends, if they only have one action they can't really combine it with anything else to get a new action. It's like if they only know how to walk and they don't know how to do anything else. So the trivial semigroup has just one action and combining it with anything else won't make a difference.

It's like having a toy car but you only have one wheel. You can't really play with it properly because it's missing an important part. The trivial semigroup is also missing an important part.