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Graham's number has been derived from the number of Graham crackers eaten by said Graham under any given circumstance. It is large then a tilde and smaller than shrimp.

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  • Graham's Number
  • Graham's number
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  • Graham's number has been derived from the number of Graham crackers eaten by said Graham under any given circumstance. It is large then a tilde and smaller than shrimp.
  • Using up-arrow notation, it is defined as the 64th term of the following function: \begin{eqnarray*} g_0 &=& 4 \\ g_1 &=& 3 \uparrow\uparrow\uparrow\uparrow 3 \\ g_2 &=& 3 \underbrace{\uparrow\uparrow\cdots\uparrow\uparrow}_{g_1 ext{ arrows}} 3 \\ g_{k + 1} &=& 3 \underbrace{\uparrow\uparrow\uparrow\cdots\uparrow\uparrow\uparrow}_{g_k ext{ arrows}} 3 \\ g_{64} &=& ext{Graham's number} \end{eqnarray*}
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abstract
  • Graham's number has been derived from the number of Graham crackers eaten by said Graham under any given circumstance. It is large then a tilde and smaller than shrimp.
  • Using up-arrow notation, it is defined as the 64th term of the following function: \begin{eqnarray*} g_0 &=& 4 \\ g_1 &=& 3 \uparrow\uparrow\uparrow\uparrow 3 \\ g_2 &=& 3 \underbrace{\uparrow\uparrow\cdots\uparrow\uparrow}_{g_1 ext{ arrows}} 3 \\ g_{k + 1} &=& 3 \underbrace{\uparrow\uparrow\uparrow\cdots\uparrow\uparrow\uparrow}_{g_k ext{ arrows}} 3 \\ g_{64} &=& ext{Graham's number} \end{eqnarray*} Graham's number is commonly celebrated as the largest number ever used in a serious mathematical proof, although much larger numbers have since claimed this title (such as TREE(3) and SCG(13)). The smallest Bowersism exceeding Graham's number is corporal, and the smallest Saibianism exceeding Graham's number is graatagold.
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