Trivial group

Hi there! A trivial group is a special type of group that only has one element.

Let's imagine you have a toy box filled with different kinds of toys like dolls, teddy bears, and action figures. Now, imagine you sort all the toys into groups based on their characteristics, like size, color, or type. For example, you could have a group of all the small red toys, or a group of all the dolls in the toy box.

A group is pretty similar to this idea. Only, instead of toys, we use mathematical objects called elements. In a group, these elements are grouped together based on some rule. This rule tells us how to combine any two elements in the group to get a third element. This is called the operation of the group.

Now, let's imagine you have a group that only has one element - this is called a trivial group. It's like having a group consisting of only one toy in your toy box. And just like how you can't really compare one toy to itself, there's only one possible way to combine the only element in a trivial group, and that's to get the same element.

So, to summarize, a trivial group is a group that has only one element, and the only operation in this group is to combine this element with itself to get the same element again.