The asankhyeya (also called asaṃkhyeya[1]) is a number described in Buddhist texts that is equal to \(10^{140}\), or 1 followed by 140 zeroes.[2] It is pronounced Asougi in Japanese where it is equal to \(10^{56}\), and means "innumerable".
The Avatamsaka Sutra [1] gives an alternate description of Asankhyeya as \(10^{7\times2^{103}}\), defining a series of numbers that are squares of each other starting with one koti equalling \(10^7\), one koti kotis making an ayuta (\(10^{14}\)), one ayuta ayutas making a nayuta (\(10^{28}\)), and so on, with Asankhyeya being the 104th number in this chain.
Approximations
For 10140:
| Notation | Lower bound | Upper bound |
|---|---|---|
| Scientific notation | \(1\times10^{140}\) | |
| Arrow notation | \(10\uparrow140\) | |
| Steinhaus-Moser Notation | 74[3] | 75[3] |
| Copy notation | 9[140] | 1[141] |
| Taro's multivariable Ackermann function | A(3,462) | A(3,463) |
| Pound-Star Notation | #*(1,2,8,11,9,8,5)*12 | #*(4,4,10,5,7,2,5,2)*10 |
| BEAF | {10,140} | |
| Hyper-E notation | E140 | |
| Bashicu matrix system | (0)(0)(0)(0)(0)[23713] | (0)(0)(0)(0)(0)[23714] |
| Hyperfactorial array notation | 90! | 91! |
| Fast-growing hierarchy | \(f_2(456)\) | \(f_2(457)\) |
| Hardy hierarchy | \(H_{\omega^2}(456)\) | \(H_{\omega^2}(457)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega^2+\omega4}}(10)\) | |
For 107×2103:
| Notation | Lower bound | Upper bound |
|---|---|---|
| Arrow notation | \((10\uparrow7)\uparrow2\uparrow103\) | |
| Down-arrow notation | \(57\downarrow\downarrow19\) | \(715\downarrow\downarrow12\) |
| Steinhaus-Moser Notation | 22[3][3] | 23[3][3] |
| Copy notation | 6[6[32]] | 7[7[32]] |
| H* function | H(23H(9)) | H(24H(9)) |
| Taro's multivariable Ackermann function | A(3,A(3,104)) | A(3,A(3,105)) |
| Pound-Star Notation | #*((1))*(1,10,10)*4 | #*((1))*(5,2,1)*6 |
| BEAF | {{10,7},{2,103}} | |
| Hyper-E notation | E(7E[2]103) | |
| Bashicu matrix system | (0)(1)[10] | (0)(1)[11] |
| Hyperfactorial array notation | (28!)! | (29!)! |
| Fast-growing hierarchy | \(f_2(f_2(100))\) | \(f_2(f_2(101))\) |
| Hardy hierarchy | \(H_{\omega^22}(100)\) | \(H_{\omega^22}(101)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega^{\omega3+1}7}}(10)\) | \(g_{\omega^{\omega^{\omega3+1}8}}(10)\) |
Sources
- ↑ 1.0 1.1 "How large is one Asamkhyeya?" Bodhi Field. http://www.drbachinese.org/vbs/publish/462/vbs462p042.pdf
- ↑ [1]
See also
Fish numbers: Fish number 1 · Fish number 2 · Fish number 3 · Fish number 4 · Fish number 5 · Fish number 6 · Fish number 7
Mapping functions: S map · SS map · S(n) map · M(n) map · M(m,n) map
By Aeton: Okojo numbers · N-growing hierarchy
By BashicuHyudora: Primitive sequence number · Pair sequence number · Bashicu matrix system
By Kanrokoti: KumaKuma ψ function
By 巨大数大好きbot: Flan numbers
By Jason: Irrational arrow notation · δOCF · δφ · ε function
By mrna: 段階配列表記 · 降下段階配列表記 · 多変数段階配列表記 · SSAN · S-σ
By Nayuta Ito: N primitive
By p進大好きbot: Large Number Garden Number
By Yukito: Hyper primitive sequence system · Y sequence · YY sequence · Y function
Indian counting system: Lakh · Crore · Tallakshana · Uppala · Dvajagravati · Paduma · Mahakathana · Asankhyeya · Dvajagranisamani · Vahanaprajnapti · Inga · Kuruta · Sarvanikshepa · Agrasara · Uttaraparamanurajahpravesa · Avatamsaka Sutra · Nirabhilapya nirabhilapya parivarta
Chinese, Japanese and Korean counting system: Wan · Yi · Zhao · Jing · Gai · Zi · Rang · Gou · Jian · Zheng · Zai · Ji · Gougasha · Asougi · Nayuta · Fukashigi · Muryoutaisuu
Other: Taro's multivariable Ackermann function · TR function · Arai's \(\psi\) · Sushi Kokuu Hen
