Fast-growing functions

Fast-growing functions are mathematical tools that increase in value very rapidly as their input grows larger. Unlike simple functions, such as addition or multiplication, these functions might double, triple, or exponentially increase with each step, making their values skyrocket quickly. They are used to understand processes or systems where growth is extremely rapid, like certain algorithms in computer science or theoretical limits in mathematics. Essentially, they help quantify and analyze situations where small increases in input lead to enormous increases in output, highlighting the concept of exponential or beyond-exponential growth.