N-ary group

An n-ary group is kind of like having a group of n friends who all like to play games together. In this group, there are some rules that they have to follow when they play together.

For example, if they are playing a game where they have to put things in a certain order, they can only move one thing at a time. Also, they have to make sure that when they move something, the order of the things doesn't get messed up.

These rules help them play their games fairly and have fun together. In a similar way, an n-ary group is a group of objects (like numbers or symbols) that have their own set of rules that they have to follow when they interact with each other.

These rules are called group axioms, and they include things like the associative property (which means that the order in which you do things doesn't matter) and the existence of an identity element (which is like having a "neutral" object that doesn't change anything when you interact with it).

By following these group axioms, the objects in an n-ary group can work together and solve problems in a fair and efficient way.