Bringing It All Together: What Makes a Group?

To sum up, A set $\mathbb{S}$ with an operation $o$ $(\mathbb{S}, o)$ is a Group If and Only if it satisfies these four properties

• Closure: Combining any two elements produces another element in the set.
• Associativity: The way you group elements doesn't change the result.
• Identity Element: There's an element that doesn't change other elements when combined.
• Inverse Element: Every element has a counterpart that combines with it to produce the identity element.