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ConceptKnuth's Up-arrow Notation

Knuth's Up-Arrow Notation

A mathematical notation for representing extremely large numbers, in which up-arrows iterate exponentiation. A single arrow denotes exponentiation, two arrows denote repeated exponentiation, and each additional arrow denotes iteration of the preceding operation. Introduced by Donald Knuth, the notation is used in the study of large numbers and in computability and recursion theory.

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Oct 13

The definition of Graham's number is: g₁ = 3↑↑↑↑3, gₙ = 3 with gₙ₋₁ arrows, and Graham's number is g₆₄.

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