Semigroup

A semigroup is like a collection of toys that you can play with, but there is a rule that you have to follow. The rule is that you can only play with one toy at a time and you can only put the toys together in a certain way.

For example, you have blocks that you can stack together, but you can only stack one block at a time. You also have marbles that you can roll, but you can only roll one marble at a time. If you follow these rules, you can have a lot of fun playing with the toys.

In math, a semigroup is similar. It is a set of elements that follow a rule when you combine them together. You can combine two elements in the set to get a third element, but you can only combine one at a time. This rule is called the semigroup operation.

For example, let's say we have a set of numbers: {1, 2, 3, 4, 5}. The addition operation (+) can be used as the semigroup operation.

If we combine 1 and 2, we get 3. If we combine 3 and 4, we get 7. If we combine 3 and 5, we get 8. And so on.

Just like with toys, if we follow the rule of the semigroup operation, we can have a lot of fun combining elements together and creating new ones.