Asymptotic analysis

Asymptotic analysis is the study of the limiting behavior of mathematical functions as their arguments approach infinity or some critical value. In algorithmic analysis, it provides the theoretical foundation for Big O notation and its variants, enabling proofs about scalability that are independent of machine-specific constants. The method's power lies in its abstraction, but that same abstraction is its weakness: by discarding lower-order terms and constants, asymptotic analysis can mislead about real-world performance on finite inputs where those "negligible" terms dominate.