Knuth paper-stack notation is an idea mentioned by Randall Munroe, creator of webcomic xkcd[1].

Definition

  1. Write the number on a stack of paper. If the stack doesn't fit in the room, move to step 2:
  2. Write the number of pages required to write the number from the previously executed step on a stack of paper. If the stack doesn't fit, repeat step 2 until it fits.
  3. When the stack finally fits, write the total number of iterations of step 2 on a card, and pin the card to the stack.

Assuming the card can fit 500 or so digits, this method can approximate numbers up to about \(10\uparrow\uparrow(10^{500})\) using Arrow notation.

Sources

  1. Xkcd, Comic 1162 (2013)
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