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Large numbers, Knuth's arrow notation, and Ramsey theory

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Abstract

In the children's book ``The Phantom Tollbooth'' by Norton Juster one can find the following passage:

``Yes, please,'' said Milo. ``Can you show me the biggest number there is?''

``I'd be delighted,'' [the Mathemagician] replied, opening one of the closet doors. ``We keep it right here. It took four miners just to dig it out.''

Inside was the biggest 3Milo had ever seen. It was fully twice as high as the Mathemagician.

This is what children might consider to be a large number. The scope of this paper is to shed some light on numbers which adults – in former times and now – regard as large. Of course, the selection is arbitrary.

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Prömel, H.J. Large numbers, Knuth's arrow notation, and Ramsey theory. Synthese 133, 87–105 (2002). https://doi.org/10.1023/A:1020879709125

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