Kleene's recursive function theory

Kleene's recursive function theory explores which functions can be computed by algorithms, essentially defining the limits of what machines can accomplish. It identifies basic functions and rules for building more complex ones through processes like composition, recursion, and minimization. These functions are called “recursive” because they can be calculated if given enough time and resources. The theory helps distinguish problems solvable by algorithms from those that are inherently unsolvable, forming a foundation for understanding computational capabilities and limitations in computer science.