WIP

Operator names

Basic level

• Binariation: x{0} = 2^x

  • Double binariation: x{0}{0} = 2^2^x

  • Triple binariation: x{0}{0}{0} = 2^2^2^x

  • Quadruple binariation: x{0}{0}{0}{0} = 2^2^2^2^x

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• Hapax-binariation: x{1} = x{0}{0}{0}...{0}{0}{0} (w/ x {0}'s) = 2^2^2^...^2^2^2^x (w/ x 2^'s)

• Dis-binariation: x{2} = x{1}{1}{1}...{1}{1}{1} (w/ x {1}'s)

• Tris-binariation: x{3} = x{2}{2}{2}...{2}{2}{2} (w/ x {2}'s)

• Tetrakis-binariation: x{4} = x{3}{3}{3}...{3}{3}{3} (w/ x {3}'s)

• Pentakis-binariation: x{5}

• Hexakis-binariation: x{6}

• Heptakis-binariation: x{7}

• Octakis-binariation: x{8}

• Enneakis-binariation: x{9}

• Decakis-binariation: x{10}

• Dodecakis-binariation: x{12}

• Hexadecakis-binariation: x{16}

• Icosakis-binariation: x{20}

• Triacontakis-binariation: x{30}

• Tessaracontakis-binariation: x{40}

• Hecatontakis-binariation: x{100}

• Chiliakis-binariation: x{1000}

• Myriakis-binariation: x{10000}

Nested primitive level

Double nests

{{1}} series

• Expansion: x{{1}} = x{x}

• Hapaka-expansion: x{{1} + 1} = x{{1}}{{1}}{{1}}...{{1}}{{1}}{{1}} (w/ x {{1}}'s)

• Dis-expansion: x{{1} + 2}

• Tris-expansion: x{{1} + 3}

• Tetrakis-expansion: x{{1} + 4}

• Pentakis-expansion: x{{1} + 5}

• Hexakis-expansion: x{{1} + 6}

• Decakis-expansion: x{{1} + 10}

• Hecatontakis-expansion: x{{1} + 100}

{{1}.2} series

• Explosion: x{{1}.2} = x{{1}{1}} = x{{1} + x}

• Hapaka-explosion: x{{1}.2 + 1} = x{{1}{1} + 1}

• Dis-explosion: x{{1}.2 + 2} = x{{1}{1} + 2}

• Tris-explosion: x{{1}.2 + 3} = x{{1}{1} + 3}

• Tetrakis-explosion: x{{1}.2 + 4} = x{{1}{1} + 4}

• Decakis-explosion: x{{1}.2 + 10} = x{{1}{1} + 10}

• Detonation: x{{1}.3} = x{{1}{1}{1}} = x{{1}{1} + x}

• Hapaka-detonation: x{{1}.3 + 1} = x{{1}{1}{1} + 1}

• Dis-detonation: x{{1}.3 + 2} = x{{1}{1}{1} + 2}

• Tris-detonation: x{{1}.3 + 3} = x{{1}{1}{1} + 3}

• Tetrakis-detonation: x{{1}.3 + 4} = x{{1}{1}{1} + 4}

• Tetronation: x{{1}.4} = x{{1}{1}{1}{1}} = x{{1}{1}{1} + x}

• Hapaka-teronation: x{{1}.4 + 1} = x{{1}{1}{1}{1} + 1}

• Dis-teronation: x{{1}.4 + 2} = x{{1}{1}{1}{1} + 2}

• Pentonation: x{{1}.5} = x{{1}{1}{1}{1}{1}} = x{{1}{1}{1}{1} + x}

• Hapaka-pentonation: x{{1}.5 + 1} = x{{1}{1}{1}{1}{1} + 1}

• Hexonation: x{{1}.6} = x{{1}{1}{1}{1}{1}{1}} = x{{1}{1}{1}{1}{1} + x}

• Heptonation: x{{1}.7}

• Octonation: x{{1}.8}

• Ennonation: x{{1}.9}

• Deconation: x{{1}.10}

• Dodeconation: x{{1}.12}

• Hexadeconation: x{{1}.16}

• Icosonation: x{{1}.20}

• Triacontonation: x{{1}.30}

• Tessaracontonation: x{{1}.40}

• Hecatontonation: x{{1}.100}

• Chilonation: x{{1}.1000}

• Myronation: x{{1}.10000}

{{2}} series

• Eruption: x{{2}} = x{{1}.x}

• Hapaka-eruption: x{{2} + 1}

• Dis-eruption: x{{2} + 2}

• Tris-eruption: x{{2} + 3}

• Tetrakis-eruption: x{{2} + 4}

• Expando-eruption: x{{2}{1}} = x{{2} + x}

• Hapaka-expando-eruption: x{{2}{1} + 1}

• Dis-expando-eruption: x{{2}{1} + 1}

• Explodo-eruption: x{{2}{1}.2} = x{{2}{1}{1}}

• Hapaka-explodo-eruption: x{{2}{1}.2 + 1} = x{{2}{1}{1} + 1}

• Detono-eruption: x{{2}{1}.3} = x{{2}{1}{1}{1}}

• Tetrono-eruption: x{{2}{1}.4} = x{{2}{1}{1}{1}{1}}

• Pentono-eruption: x{{2}{1}.5} = x{{2}{1}{1}{1}{1}{1}}

• Hexono-eruption: x{{2}{1}.6} = x{{2}{1}{1}{1}{1}{1}{1}}

• Ebullition: x{{2}.2} = x{{2}{2}} = x{{2}{1}.x}

• Hapaka-ebullition: x{{2}.2 + 1} = x{{2}{2} + 1}

• Dis-ebullition: x{{2}.2 + 2} = x{{2}{2} + 2}

• Expando-ebullition: x{{2}.2 {1}} = x{{2}{2}{1}} = x{{2}{2} + x}

• Hapaka-expando-ebullition: x{{2}.2 {1} + 1} = x{{2}{2}{1} + 1}

• Explodo-ebullition: x{{2}.2 {1}.2} = x{{2}{2}{1}{1}}

• Detono-ebullition: x{{2}.2 {1}.3} = x{{2}{2}{1}{1}{1}}

• Tetrono-ebullition: x{{2}.2 {1}.4} = x{{2}{2}{1}{1}{1}{1}}

• Trebullition: x{{2}.3} = x{{2}{2}{2}} = x{{2}{2}{1}.x}

• Hapaka-trebullition: x{{2}.3 + 1} = x{{2}{2}{2} + 1}

• Expando-trebullition: x{{2}.3 {1}} = x{{2}{2}{2}{1}}

• Explodo-trebullition: x{{2}.3 {1}.2} = x{{2}{2}{2}{1}{1}}

• Tetrebullition: x{{2}.4} = x{{2}{2}{2}{2}}

• Pentebullition: x{{2}.5} = x{{2}{2}{2}{2}{2}}

• Hexebullition: x{{2}.6} = x{{2}{2}{2}{2}{2}{2}}

• Dekebullition: x{{2}.10}

• Icosebullition: x{{2}.20}

• Hecatontebullition: x{{2}.100}

• Chilebullition: x{{2}.1000}

{{3}} series

• Generation = x{{3}} = x{{2}.x}

• Hapaka-generation = x{{3} + 1}

• Dis-generation = x{{3} + 2}

• Expando-generation = x{{3}{1}} = x{{3} + x}

• hapaka-expando-generation = x{{3}{1} + 1}

• Explodo-generation = x{{3}{1}.2} = x{{3}{1}{1}}

• Detono-generation = x{{3}{1}.3} = x{{3}{1}{1}{1}}

• Tetrono-generation = x{{3}{1}.4} = x{{3}{1}{1}{1}{1}}

• Eruptive-generation = x{{3}{2}} = x{{3}{1}.x}

• Hapaka-eruptive-generation = x{{3}{2} + 1}

• Expando-eruptive-generation = x{{3}{2}{1}}

• Explodo-eruptive-generation = x{{3}{2}{1}.2} = x{{3}{2}{1}{1}}

• Ebullient-generation = x{{3}{2}.2} = x{{3}{2}{2}}

• Expando-ebullient-generation = x{{3}{2}.2 {1}} = x{{3}{2}{2}{1}}

• Trebullient-generation = x{{3}{2}.3} = x{{3}{2}{2}{2}}

• Tetrebullient-generation = x{{3}{2}.4} = x{{3}{2}{2}{2}{2}}

• Pentebullient-generation = x{{3}{2}.5} = x{{3}{2}{2}{2}{2}{2}}

• Hexebullient-generation = x{{3}{2}.6} = x{{3}{2}{2}{2}{2}{2}{2}}

• Deutero-generation = x{{3}.2} = x{{3}{3}} = x{{3}{2}.x}

• Hapaka-deutero-generation = x{{3}.2 + 1} = x{{3}{3} + 1}

• Expando-deutero-generation = x{{3}.2 {1}} = x{{3}{3}{1}}

• Explodo-deutero-generation = x{{3}.2 {1}.2} = x{{3}{3}{1}{1}}

• Eruptive-deutero-generation = x{{3}.2 {2}} = x{{3}{3}{2}}

• Expando-eruptive-deutero-generation = x{{3}.2 {2}{1}} = x{{3}{3}{2}{1}}

• Ebullient-deutero-generation = x{{3}.2 {2}.2} = x{{3}{3}{2}{2}}

• Trebullient-deutero-generation = x{{3}.2 {2}.3} = x{{3}{3}{2}{2}{2}}

• Trito-generation = x{{3}.3} = x{{3}{3}{3}}

• Expando-trito-generation = x{{3}.3 {1}} = x{{3}{3}{3}{1}}

• Eruptive-trito-generation = x{{3}.3 {2}} = x{{3}{3}{3}{2}}

• Teterto-generation = x{{3}.4} = x{{3}{3}{3}{3}}

• Pepto-generation = x{{3}.5} = x{{3}{3}{3}{3}{3}}

• Exto-generation = x{{3}.6} = x{{3}{3}{3}{3}{3}{3}}

• Epto-generation = x{{3}.7}

• Ogdo-generation = x{{3}.8}

• Ento-generation = x{{3}.9}

• Dekato-generation = x{{3}.10}

• Icosto-generation = x{{3}.20}

• Hecato-generation = x{{3}.100}

• Chilio-generation = x{{3}.1000}

{{4+}} series

• Construction = x{{4}} = x{{3}.x}

• Hapaka-construction = x{{4} + 1}

• Expando-construction = x{{4}{1}}

• Explodo-construction = x{{4}{1}.2} = x{{4}{1}{1}}

• Eruptive-construction = x{{4}{2}}

• Ebullient-construction = x{{4}{2}.2} = x{{4}{2}{2}}

• Generative-construction = x{{4}{3}}

• Eruptive-generative-construction = x{{4}{3}{2}}

• Deutero-generative-construction = x{{4}{3}.2} = x{{4}{3}{3}}

• Trito-generative-construction = x{{4}{3}.3} = x{{4}{3}{3}{3}}

• Teterto-generative-construction = x{{4}{3}.4} = x{{4}{3}{3}{3}{3}}

• Deutero-construction = x{{4}.2} = x{{4}{4}}

• Hapaka-deutero-construction = x{{4}.2 + 1} = x{{4}{4} + 1}

• Expando-deutero-construction = x{{4}.2 {1}} = x{{4}{4}{1}}

• Eruptive-deutero-construction = x{{4}.2 {2}} = x{{4}{4}{2}}

• Generative-deutero-construction = x{{4}.2 {3}} = x{{4}{4}{3}}

• Trito-construction = x{{4}.3} = x{{4}{4}{4}}

• Eruptive-trito-construction = x{{4}.3 {2}} = x{{4}{4}{4}{2}}

• Generative-trito-construction = x{{4}.3 {3}} = x{{4}{4}{4}{3}}

• Teterto-construction = x{{4}.4} = x{{4}{4}{4}{4}}

• Pepto-construction = x{{4}.5} = x{{4}{4}{4}{4}{4}}

• Exto-construction = x{{4}.6} = x{{4}{4}{4}{4}{4}{4}}

• Dekato-construction = x{{4}.10}

• Creation = x{{5}}

• Hapaka-creation = x{{5} + 1}

• Explodo-creation = x{{5}{1}}

• Eruptive-creation = x{{5}{2}}

• Generative-creation = x{{5}{3}}

• Deutero-generative-creation = x{{5}{3}.2} = x{{5}{3}{3}}

• Constructive-creation = x{{5}{4}}

• Deutero-constructive-creation = x{{5}{4}.2} = x{{5}{4}{4}}

• Trito-constructive-creation = x{{5}{4}.3} = x{{5}{4}{4}{4}}

• Deutero-creation = x{{5}.2} = x{{5}{5}}

• Generative-deutero-creation = x{{5}.2 {3}} = x{{5}{5}{3}}

• Constructive-deutero-creation = x{{5}.2 {4}} = x{{5}{5}{4}}

• Trito-creation = x{{5}.3} = x{{5}{5}{5}}

• Teterto-creation = x{{5}.4} = x{{5}{5}{5}{5}}

• Pepto-creation = x{{5}.5} = x{{5}{5}{5}{5}{5}}

• Exto-creation = x{{5}.6} = x{{5}{5}{5}{5}{5}{5}}

• Formation = x{{6}} = x{{5}.x}

• Eruptive-formation = x{{6}{2}}

• Generative-formation = x{{6}{3}}

• Constructive-formation = x{{6}{4}}

• Creative-formation = x{{6}{5}}

• Deutero-creative-formation = x{{6}{5}.2} = x{{6}{5}{5}}

• Deutero-formation = x{{6}.2} = x{{6}{6}}

• Creative-deutero-formation = x{{6}.2 {5}} = x{{6}{6}{5}}

• Trito-formation = x{{6}.3} = x{{6}{6}{6}}

• Teterto-formation = x{{6}.4} = x{{6}{6}{6}{6}}

• Heptaformation = x{{7}} = x{{6}.x}

• Constructive-heptaformation = x{{7}{4}}

• Creative-heptaformation = x{{7}{5}}

• Formative-heptaformation = x{{7}{6}}

• Deutero-heptaformation = x{{7}.2} = x{{7}{7}}

• Trito-heptaformation = x{{7}.3} = x{{7}{7}{7}}

• Octaformation = x{{8}} = x{{7}.x}

• Formative-octaformation = x{{8}{6}}

• Heptaformative-octaformation = x{{8}{7}}

• Deutero-octaformation = x{{8}.2} = x{{8}{8}}

• Trito-octaformation = x{{8}.3} = x{{8}{8}{8}}

• Enneaformation = x{{9}} = x{{8}.x}

• Octaformative-enneaformation = x{{9}{8}}

• Deutero-enneaformation = x{{9}.2} = x{{9}{9}}

• Decaformation = x{{10}} = x{{9}.x}

• Deutero-decaformation = x{{10}.2} = x{{10}{10}}

• Endecaformation = x{{11}}

• Dodecaformation = x{{12}}

• Hexadecaformation = x{{16}}

• Icosaformation = x{{20}}

• Triacontaformation = x{{30}}

• Tessaracaformation = x{{40}}

• Hecatontaformation = x{{100}}

• Chilaformation = x{{1000}}

• Myriaformation = x{{10000}}

Triple nests

{{{1}}} series

• Lineation = x{{{1}}} = x{{x}}

• Lineata-hapaxation = x{{{1}} + 1}

• Lineata-disation = x{{{1}} + 2}

• Lineata-trisation = x{{{1}} + 3}

• Lineata-tetrakisation = x{{{1}} + 4}

• Lineata-expansion = x{{{1}}{1}} = x{{{1}} + x}

• Lineata-hapaka-expansion = x{{{1}}{1} + 1}

• Lineata-explosion = x{{{1}}{1}.2} = x{{{1}}{1}{1}}

• Lineata-detonation = x{{{1}}{1}.3} = x{{{1}}{1}{1}{1}}

• Lineata-tetronation = x{{{1}}{1}.4} = x{{{1}}{1}{1}{1}{1}}

• Lineata-eruption = x{{{1}}{2}} = x{{{1}}{1}.x}

• Lineata-hapaka-eruption = x{{{1}}{2} + 1}

• Lineata-expando-eruption = x{{{1}}{2}{1}}

• Lineata-ebullition = x{{{1}}{2}.2} = x{{{1}}{2}{2}}

• Lineata-trebullition = x{{{1}}{2}.3} = x{{{1}}{2}{2}{2}}

• Lineata-generation = x{{{1}}{3}} = x{{{1}}{2}.x}

• Lineata-deutero-generation = x{{{1}}{3}.2} = x{{{1}}{3}{3}}

• Lineata-construction = x{{{1}}{4}} = x{{{1}}{3}.x}

• Lineata-creation = x{{{1}}{5}}

• Lineata-formation = x{{{1}}{6}}

{{{1}}.2} series

• Deutero-lineation = x{{{1}}.2} = x{{{1}}{{1}}} = x{{{1}}{x}}

• Deutero-lineata-hapaxation = x{{{1}}.2 + 1} = x{{{1}}{{1}} + 1}

• Deutero-lineata-expansion = x{{{1}}.2 {1}} = x{{{1}}{{1}}{1}}

• Deutero-lineata-eruption = x{{{1}}.2 {2}} = x{{{1}}{{1}}{2}}

• Deutero-lineata-generation = x{{{1}}.2 {3}} = x{{{1}}{{1}}{3}}

• Trito-lineation = x{{{1}}.3} = x{{{1}}{{1}}{{1}}} = x{{{1}}{{1}}{x}}

• Trito-lineata-hapaxation = x{{{1}}.3 + 1} = x{{{1}}{{1}}{{1}} + 1}

• Trito-lineata-expansion = x{{{1}}.3 {1}} = x{{{1}}{{1}}{{1}}{1}}

• Teterto-lineation = x{{{1}}.4} = x{{{1}}{{1}}{{1}}{{1}}}

• Pepto-lineation = x{{{1}}.5} = x{{{1}}{{1}}{{1}}{{1}}{{1}}}

• Exto-lineation = x{{{1}}.6} = x{{{1}}{{1}}{{1}}{{1}}{{1}}{{1}}}

{{{1} + 1}} series

• Hapa-lineation = x{{{1} + 1}} = x{{{1}}.x}

• Deutero-hekelineation = x{{{1} + 1}.2} = x{{{1} + 1}{{1} + 1}}

• Dya-lineation = x{{{1} + 2}} = x{{{1} + 1}.x}

• Trya-lineation = x{{{1} + 3}}

• Tetrakia-lineation = x{{{1} + 4}}

• Pentakia-lineation = x{{{1} + 5}}

• Hexakia-lineation = x{{{1} + 6}}

{{{1}.2}} series

• Lineadeusation = x{{{1}.2}} = x{{{1}{1}}} = x{{{1} + x}}

• Hapa-lineadeusation = x{{{1}.2 + 1}} = x{{{1}{1} + 1}} = x{{{1}{1}}.x}

• Dya-lineadeusation = x{{{1}.2 + 2}} = x{{{1}{1} + 2}}

• Trya-lineadeusation = x{{{1}.2 + 3}} = x{{{1}{1} + 3}}

• Lineatrusation = x{{{1}.3}} = x{{{1}{1}{1}}} = x{{{1}{1} + x}}

• Hapa-lineatrusation = x{{{1}.3 + 1}} = x{{{1}{1}{1} + 1}}

• Lineaquadation = x{{{1}.4}} = x{{{1}{1}{1}{1}}} = x{{{1}{1}{1} + x}}

• Lineaquidation = x{{{1}.5}} = x{{{1}{1}{1}{1}{1}}}

• Lineasidation = x{{{1}.6}} = x{{{1}{1}{1}{1}{1}{1}}}

• Lineaseptusation = x{{{1}.7}}

• Lineaoctusation = x{{{1}.8}}

• Lineanonisation = x{{{1}.9}}

• Lineadecisation = x{{{1}.10}}

• Lineavigintisation = x{{{1}.20}}

• Lineacentisation = x{{{1}.100}}

• Lineamillisation = x{{{1}.1000}}

{{{2}}} series

• Gridation = x{{{2}}} = x{{{1}.x}}

{{{3+}}} series

• Cubilation = x{{{3}}} = x{{{2}.x}}

• Quartilation = x{{{4}}} = x{{{3}.x}}

• 
  

Quadruple nests

{{{{1}}}} series

• Tetrisation = x{{{{1}}}} = x{{{x}}}

{{{{1} + 1}}} series

{{{{1}.2}}} series

{{{{2+}}}} series

Higher nests

{{{{{1}}}}} series

• Pentisation = x{{{{{1}}}}} = x{{{{x}}}}

{{{{{2}}}}} series

Sextuple nest series

Septuple nest series

Octuple nest series and higher

Pair sequence level

/// VERY WIP ///

• Primation = x{{0, 1}} = x{{{…{{{0}}}…}}} (w/ x nests of brackets) = x{{{…{{{1}}}…}}} (w/ x-1 nests of brackets) = x{{{…{{{x}}}…}}} (w/ x-2 nests of brackets)