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The -yllion system is a fabricated system invented by Donald Knuth for naming large numbers.[1]

Usage

Numbers up to 999 are named as they are normally.

Numbers from 1000 to 9999 are written without a comma and pronounced "a-ty b hundred c-ty d" for the number abcd. For example, 7283 is pronounced "seventy-two hundred eighty-three." The word thousand is not used in this system.

\(10^4\) is called the myriad. All numbers from the myriad up to 9999,9999 are written with a comma between the ten thousands and thousands place. For example, 54325 would be written 5,4325.

Such numbers are pronounced like so:

  • 45,7839 is pronounced "forty-five myriad seventy-eight hundred thirty-nine."
  • 2423,3000 is pronounced "twenty-four hundred twenty-three myriad thirty hundred."
  • 9999,9999 is pronounced "ninety-nine hundred ninety-nine myriad ninety-nine hundred ninety-nine."

\(10^8\) is called the myllion. It is written 1;0000,0000. Note that a new punctuation mark, a semicolon, was used to represent the myllions place. Numbers up to 9999,9999;9999,9999 are named in the same way as the above numbers are pronounced: each group of four digits is pronounced as written above, and the commas are pronounced "myriad." The only difference is that the semicolon (;) is pronounced "myllion."

\(10^{16}\) is called the byllion. It is written 1:0000,0000;0000,0000. Note that a new punctuation mark, a colon, was used to represent the byllions place. Numbers up to 9999,9999;9999,9999:9999,9999;9999,9999 are pronounced as above, but the colon (:) is pronounced "byllion."

Continuing in this method, we have n-yllion \(= 10^{2^{n+2}}\), allowing the tryllion, quadryllion, quintyllion, etc.

In googological notations

Notation Upper bound Condition
Fast-growing hierarchy \(f_2^2(n)\) \(n>13\)
Hardy hierarchy \(H_{\omega^2 2}(n)\) \(n>13\)
Slow-growing hierarchy \(g_{\omega^{\omega^\omega}}(n)\) \(n>3\)

Sources

See also

The Chinese numeral system also had one scale in which each symbol was the square of the next.


Myriad System Numbers myllion · byllion · tryllion · quadryllion · quintyllion · sextyllion · septyllion · octyllion · nonyllion · decyllion · undecyllion · duodecyllion · tredecyllion · quattuordecyllion · quindecyllion · sexdecyllion · septdecyllion · octodecyllion · novemdecyllion · vigintyllion · unvigintyllion · duovigintyllion · trevigintyllion · quattuorvigintyllion · quinvigintyllion · sexvigintyllion · septemvigintyllion · octovigintyllion · novemvigintyllion · trigintyllion · untrigintyllion · duotrigintyllion · tretrigintyllion · quattuortrigintyllion · quintrigintyllion · sextrigintyllion · septtrigintyllion octotrigintyllion · novemtrigintyllion · quadragintyllion · quinquagintyllion · sexagintyllion · septuagintyllion · octogintyllion · nonagintyllion · centyllion · ducentyllion · trecentyllion · quadringentyllion · quingentyllion · sescentyllion · septingentyllion · octingentyllion · nongentyllion · millyllion · myryllion · micryllion · nanyllion · picyllion · femtyllion · attyllion · zeptyllion · yoctyllion · googolyllion · latinlatinlatinbyllionyllionyllionyllion

Googological affixes

Suffixes: -teen · -ty · -plex · -illion · -yllion · -exian · -chime · -toll · -gong · -bong · -throng · -illiob
Prefixes: gar- · fz- · fuga- · megafuga- · booga- · trooga- · googo- · googolple-
SI prefixes: deca- · hecto- · kilo- · mega- · giga- · tera- · peta- · exa- · zetta- · yotta-
Obsolete SI prefixes: myria-
Extended SI prefixes: 1.001 · 1.01 · 1.1 · 1.5 · 2 · 3 · 666 · 105 · 107 · 1027 · 1030 · 1033 · 1036 · 1039 · 1042 · 1045 · 1048 · 1051 · 1054 · 1057 · 1060 · 1063 · 1066 · 1069 · 1072 · 1075 · 1078 · 1081 · 1084 · 1087 · 1090 · 10100 · 10120 · 10150 · 10180 · 10210 · 10240 · 10270 · 10300 · 10600 · 10900 · 101200 · 101500 · 101800 · 102100 · 102400 · 102700 · 103000 and higher

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