Knuth's up-arrow notation is a mathematical notation introduced by Donald Knuth to represent very large numbers. It uses arrows to indicate repeated operations of exponentiation. For example, a single arrow (↑) represents exponentiation, while two arrows (↑↑) denote 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 (↑↑↑) represent a process called "tetration," which is repeated application of exponentiation. This system allows mathematicians to express extremely large numbers succinctly, far beyond conventional notation.