# 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.

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