Graham's Number
Version 1.0.0 · Updated 2026-07-28
CORE DEFINITION
Graham’s number is an enormous finite positive integer associated with an upper bound for a geometric Ramsey problem. Knuth’s up-arrow notation and a finite recursive definition specify it exactly. Being unable to physically write out its decimal expansion does not make it infinite or undefinable.
SCAFFOLDING EFFECT
Reduce cognitive load
Distinguishes the resources needed to define an object precisely from those needed to expand its entire representation, and a known upper bound from the actual minimum solution.
Anchor fast decisions
The recursion starts with four arrows; each term supplies the number of arrows between the two 3s in the next term, and the 64th term is selected. A finite symbolic rule specifies an integer far beyond practical expansion. An upper bound gives a sufficient dimension, not the exact minimum dimension.
MINIMUM ACTION
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Source support: Explicit
- zh.wikipedia.orghttps://zh.wikipedia.org/wiki/%E8%91%9B%E7%AB%8B%E6%81%86%E6%95%B8verified
- en.wikipedia.orghttps://en.wikipedia.org/wiki/Graham%27s_numberverified
- mathworld.wolfram.comhttps://mathworld.wolfram.com/GrahamsNumber.htmlverified
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