Definition

A collection of elements that can be combined using a specific operation, where the combination of any two elements in the set results in another element from the same set, and the operation follows a rule of associativity.

Example

In algebra, a semigroup is often used to study the properties of certain mathematical structures.

Conversation

Have you ever heard of a semigroup?

Yeah, I think it's a concept in mathematics, right?

Exactly! It's a set that has some interesting properties.

That sounds cool! I love how math has these unique structures.

Synonyms & Antonyms

Root Explanation

Semigroup → It is formed from "semi-" (meaning half or partially) and "group" (from Greek "groupus", meaning a collection or assembly). A semigroup is a partially defined group, where the operation is associative but not necessarily having an identity element.

Memory Tip

Think of 'semi-' meaning partially, and 'group' referring to a collection. This helps you remember that a semigroup is a collection that is partially defined.

Visually Confused Words