Japanese characters for muryoutaisuu

Muryoutaisuu (無量大数 written in Japanese, means "large number without measure") is \(10^{68}\) in Japanese counting system[1][2]. It was derived from Chinese counting system, which was derived from Buddism's sutra in India. There are several different versions of counting systems in Chinese, meaning different numbers for the same Chinese character but different pronunciation[3].

It first appeared in Jinkouki (Japanese: 塵劫記) by Mitsuyoshi Yoshida in 1631. In the first edition of Jinkouki published in 1627, numbers up to Fukashigi was defined, and muryoutaisuu did not appear. In the 1631 edition of Jinkouki, definition of Muryoutaisuu was \(10^{88}\), and later in the 1634 edition of Jinkouki, definition changed to \(10^{68}\). Therefore, the definition of Muryoutaisuu is now \(10^{68}\).

In English, it is one hundred unvigintillion in short scale and one hundred undecillion in long scale.

The total mass-energy of the observable universe is estimated to be about 130 muryoutaisuu joules.

Approximations

Notation Lower bound Upper bound
Scientific notation \(1\times10^{68}\)
Arrow notation \(10\uparrow68\)
Steinhaus-Moser Notation 41[3] 42[3]
Copy notation 9[68] 1[69]
Taro's multivariable Ackermann function A(3,222) A(3,223)
Pound-Star Notation #*(12,0,8,4,3)*10 #*(7,0,8,6,3,1)*8
BEAF {10,68}
Hyper-E notation E68
Bashicu matrix system (0)(0)(0)(0)[17782] (0)(0)(0)(0)[17783]
Hyperfactorial array notation 52! 53!
Fast-growing hierarchy \(f_2(218)\) \(f_2(219)\)
Hardy hierarchy \(H_{\omega^2}(218)\) \(H_{\omega^2}(219)\)
Slow-growing hierarchy \(g_{\omega^{\omega6+8}}(10)\)

Sources

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

Community content is available under CC-BY-SA unless otherwise noted.