Finiteness of Regular Language

Question

We all know that (a + b)* is a regular language for containing only symbols a and b. But (a + b)* is a string of infinit

Answer 1

Each word in the language (a+b) is of finite length. The same way as there are infinitely many integers, but each of them finite.

Yes, the language itself is an infinite set. Most languages are. But a finite automaton (NB: automata is plural) works just fine for them, provided each word is of finite length.

As an aside: This type of question probably should go to cs.stackexchange.com.