I'm trying to provide a formal (mathematical) definition of regular language.
I'm defining a regular language as
Is a type of formal language that can be generated from a basic language with the application of union, concatenation and Kleene $(*)$ a finit number of times.
I'm not sure about this definition to be mathematically enough in order to define regular languages, any hint or help will be really appreciated and thank you for taking the time to read my question.
Let $A$ be a finite alphabet. The set of rational (or regular) languages on $A^*$, forms the smallest set of languages containing the languages $\{a\}$ for each letter $a \in A$, and is closed under finite union, product and star. Thus the empty language is rational (empty union) and if $L$ and $L'$ are rational languages, then the languages $L \cup L'$, $LL'$ and $L^*$ are also rational.
Note that, if $1$ denotes the empty word, then the language $\emptyset^* = \{1\}$. Thus this language is also rational.