Knuth's Up-arrow Notation is a mathematical notation introduced by Donald Knuth to express very large numbers. It uses arrows to represent repeated operations of exponentiation. For example, a single arrow (↑) denotes exponentiation, while two arrows (↑↑) represent repeated exponentiation, such as a^(a^{(a^{...)})} with a repeated n times. The notation can be extended further with more arrows. For instance, three arrows (↑↑↑) indicate a process called "tetration," which is repeated application of exponentiation. This system allows mathematicians to describe numbers that grow much faster than traditional operations can express.