Regular Language-formal definition

As I said in my previous post, we will discuss formal definitions of a single term at a time. Today, we are going to discuss “Regular languages”

Regular languages over an alphabet (Formal Definition):
The collection of regular languages over an alphabet Σ is defined recursively as follows:
 the empty language Ø is a regular language.
 the empty string language { ε } is a regular language.
 For each a ∈ Σ, the singleton language { a } is a regular language.
 If A and B are regular languages, then A ∪ B (union), A B (concatenation), and A* (Kleene star) are regular languages