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Borges' number (so named by Robert Munafo) is equal to 25410*40*80 = 251,312,000 ~ 1.9560*101,834,097.[1] It is the number of books in the Library of Babel, a fictional library which appears in a short story of the same name by Jorge Luis Borges. The Library of Babel contains every possible book with 410 pages, 40 lines per page, and 80 characters per line, with 25 different possible characters (22 letters, space, period, and comma). Among those books are every fictional story that has been written, every story that has not been written, every erroneous version or translation of one of these stories, etc., but most of those books would of course be nonsense.

Size Edit

Borges' number has about 1.8 million digits, so it is larger than a maximusmillion but smaller than a googolbong. It is a small class 3 number, but it is still a very large number, being much larger than the number of atoms or even Planck volumes in the observable universe, even if the number of Planck volumes were raised to the thousandth power. However, Borges' number is not particularly impressive by googologists' standards, as it is not even bigger than a googolplex.

ApproximationsEdit

Notation Lower bound Upper bound
Scientific notation \(1.956\times10^{1834097}\) \(1.957\times10^{1834097}\)
Arrow notation \(5\uparrow2624000\)
Steinhaus-Moser Notation 6[3][3] 7[3][3]
Copy notation 1[1[7]] 2[2[7]]
Taro's multivariable Ackermann function A(3,A(3,19)) A(3,A(3,20))
Pound-Star Notation #*((1091))*561 #*((1092))*561
BEAF {5,2624000}
Hyper-E notation E[5]2624000
Bashicu matrix system (0)(1)[19] (0)(1)[20]
Hyperfactorial array notation (8!)! (9!)!
Fast-growing hierarchy \(f_2(f_2(18))\) \(f_2(f_2(19))\)
Hardy hierarchy \(H_{\omega^22}(18)\) \(H_{\omega^22}(19)\)
Slow-growing hierarchy \(g_{\omega^{\omega^43+\omega^38+\omega^224+\omega5}}(25)\)

References Edit

  1. http://mrob.com/pub/math/numbers-20.html

See also Edit