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Ninety-nines is equal to \(9 \lfloor 10^{90} / 9\rfloor = 10^{90} - 1\), or 90 copies of 9:[1]

999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999
or metamathematically with interior superscription as \(9^{88}9\)

It is exactly googol/dialogue - 1.

Its prime factorization is 34 × 7 × 11 × 13 × 19 × 31 × 37 × 41 × 211 × 241 × 271 × 2,161 × 9,091 × 29,611 × 52,579 × 238,681 × 333,667 × 2,906,161 × 3,762,091 × 8,985,695,684,401 × 4,185,502,830,133,110,721.

Approximations

Notation Lower bound Upper bound
Scientific notation \(9.999\times10^{89}\) \(1\times10^{90}\)
Arrow notation \(111\uparrow44\) \(10\uparrow90\)
Steinhaus-Moser Notation 52[3] 53[3]
Copy notation 9[90]
Taro's multivariable Ackermann function A(3,295) A(3,296)
Pound-Star Notation #*(2,12,2,8,4,3)*10 #*(1,3,7,7,2,2,10)*7
BEAF {111,44} {10,90}
Hyper-E notation 9E89 E90
Bashicu matrix system (0)(0)(0)(0)(0)[649] (0)(0)(0)(0)(0)[650]
Hyperfactorial array notation 64! 65!
Fast-growing hierarchy \(f_2(290)\) \(f_2(291)\)
Hardy hierarchy \(H_{\omega^2}(290)\) \(H_{\omega^2}(291)\)
Slow-growing hierarchy \(g_{\omega^{\omega^2+\omega+4}2}(9)\) \(g_{\omega^{\omega9}}(10)\)

Sources

  1. Halm, Michael Joseph. neologisms. Archived from the original on 2014-02-19. Retrieved 2018-02-26.

See also

Repdigit googologisms
Numbers by André Joyce

Repunits: twenty-twos · thirty-threes · forty-fours · fifty-fives · sixty-sixes · seventy-sevens · eighty-eights · twelvety-twelves
Googo- series: googoli · googoliji · googoliv · googolv · googolvi · googolvij · googolix · googolex · googoc · googoci · googocci · googoccic · googoxem · googolmox · googomump ·
Googoo- series: googool · googoolxiv · googoolxix · googoocxexviji · googood · googoodij · googoodiv · googoodvi · googoodvij · googoodix · googoodxi
Googgoo- series: googgol · googgool · geegeel · geeggeel · geiggeil · geiggeim
Googolplux series: googolplux · googolpluc · googolplum
Bowers' numbers attempts: Joycian gaggol · Joycian gygol · Joycian gagol · Joyce's tetratri · Joyce's pentatri · Joycian grand tridecal · Joycian dimentri · Joycian dulatri · Joycian trimentri · Joycian decaltrix
Archive André Joyce archive

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