monoids

A monoid is a mathematical concept involving a set of elements combined with an operation that satisfies two key properties: closure and associativity. Closure means applying the operation to any two elements in the set results in another element within the same set. Associativity ensures that when combining three elements, the grouping doesn't affect the result. Additionally, there is an identity element in the set that, when combined with any other element, leaves it unchanged. Monoids are foundational in areas like computer science and algebra, providing a structured way to combine and relate elements systematically.