Recently, I have read something about Ackermann function and Knuth's up-arrow notation. I know that notation is used to denote vary large number. However, I can't find any practical use - the notation is applied in certain algorithms or programs - of this notation. So could anyone know is there any real-world use of this notation?
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Graham's number, one of the largest numbers ever used in serious mathematical proof, is an upper bound for a problem related to Ramsey theory. This use is not directly related to programming though.
n. m. could be an AI
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One example is the disjoint set data structure which is used in algorithms to compute connected components of graphs.
The complexity of the amortized time per operation when using this data structure is based on the inverse of the Ackermann function.
See the paper "Efficiency of a Good But Not Linear Set Union Algorithm" by R.Tarjan for the proof.
Peter de Rivaz
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