A formal system is a structured framework used in mathematics and logic to derive conclusions from a set of axioms and rules. It consists of a language, which includes symbols and syntax, and a set of inference rules that dictate how new statements can be formed from existing ones.
In a formal system, every statement can be proven true or false based on the established axioms. This concept is foundational in areas like mathematical logic and computer science, where it helps in understanding the limits of computation and the nature of mathematical proofs.
