Knuth's up-arrow notation

Knuth's up-arrow notation is a way to express extremely large numbers using a hierarchy of operations beyond exponentiation. It uses arrows to indicate the level of repetition: one arrow (↑) denotes exponentiation, two arrows (↑↑) represent tetration (iterated exponentiation), and more arrows indicate higher-level operations. For example, 3↑4 equals 3⁴, while 3↑↑4 means 3 tetrated four times, resulting in an astronomically large number. This notation provides a compact way to describe and work with enormous quantities that often surpass conventional exponential expressions.