Theories of Functions

Theories of functions explore how inputs relate to outputs in a consistent way. A function can be thought of as a rule or process that assigns exactly one output to each input. Different theories examine this concept from perspectives like set theory, algebra, or calculus, focusing on properties such as continuity, invertibility, and composition. They help us understand how functions behave, how they can be constructed, and how they relate to other mathematical objects. Essentially, these theories form the foundation for analyzing and applying functions across various areas of math and science, promoting a structured understanding of how systems respond to different inputs.