theorems of asymptotic behavior

Theorems of asymptotic behavior describe how functions or sequences behave as they grow very large or very small. They help us understand the long-term trends, like how algorithms perform as input sizes increase or how physical systems behave over time. These theorems, such as Big O notation, provide ways to compare growth rates and predict future behavior without needing exact calculations. Essentially, they show the dominant patterns that emerge when looking at extreme cases, making complex behaviors more understandable and manageable for analysis.