Groups - Motivation for Definition

The definition of a group is very abstract. We motivate this definition with a simple, concrete example from basic algebra.

Why did we need to define a group in the first place? What motivated the creation of this abstract idea, and hence, launch an entire field of mathematics (Abstract Algebra)?

Hint: what can you accomplish if a group has these characteristics?
▪ Set of elements
▪ Has an operation *
▪ Closed under that operation *
▪ Has an identity e
▪ Has inverses
▪ Associative

If you’d like to review this definition in more detail, visit The Definition of a Group. In this shorter video, we’ll provide the surprisingly simple motivation for why a group was defined in this way. More lessons and resources below.