| Function name | Existing name | Shorthand | Array equivalent | FGH growth rate (approximate) |
|---|---|---|---|---|
| Addition | a+b | f1(n) | ||
| Multiplication | a*b | f2(n) | ||
| Exponentiation | {1} | {a,b} | f3(n) | |
| Tetration | {2} | {a,b,2} | f4(n) | |
| Pentation | {3} | {a,b,3} | f5(n) | |
| Hexation | {4} | {a,b,4} | f6(n) | |
| Heptation | {5} | {a,b,5} | f7(n) | |
| Octation | {6} | {a,b,6} | f8(n) | |
| Enneation | {7} | {a,b,7} | f9(n) | |
| Decation | {8} | {a,b,8} | f10(n) | |
| Vigintation | {18} | {a,b,18} | f20(n) | |
| Trigintation | {28} | {a,b,28} | f30(n) | |
| Centation | {98} | {a,b,98} | f100(n) | |
| Chiliation | {998} | {a,b,998} | f1000(n) | |
| Myriation | {9998} | {a,b,9998} | f10000(n) | |
| Megation | {M.} | {a,a,b} | fω(n) | |
| Mega-addition | Expansion | {M.1} | {a,b,1,2} | fω+1(n) |
| Mega-multiplication | Multiexpansion | {M.2} | {a,b,2,2} | fω+2(n) |
| Mega-exponentiation | Powerexpansion | {M.3} | {a,b,3,2} | fω+3(n) |
| Mega-tetration | Expandotetration | {M.4} | {a,b,4,2} | fω+4(n) |
| Mega-pentation | {M.5} | {a,b,5,2} | fω+5(n) | |
| Mega-hexation | {M.6} | {a,b,6,2} | fω+6(n) | |
| Duomegation | {2M.} | {a,a,b,2} | fω2(n) | |
| Duomega-addition | Explosion | {2M.1} | {a,b,1,3} | fω2+1(n) |
| Duomega-multiplication | Multiexplosion | {2M.2} | {a,b,2,3} | fω2+2(n) |
| Duomega-exponentiation | Powerexplosion | {2M.3} | {a,b,3,3} | fω2+3(n) |
| Duomega-tetration | Explodotetration | {2M.4} | {a,b,4,3} | fω2+4(n) |
| Trimegation | {3M.} | {a,a,b,3} | fω3(n) | |
| Trimega-addition | Detonation | {3M.1} | {a,b,1,4} | fω3+1(n) |
| Trimega-multiplication | {3M.2} | {a,b,2,4} | fω3+2(n) | |
| Trimega-exponentiation | {3M.3} | {a,b,3,4} | fω3+3(n) | |
| Trimega-tetration | {3M.4} | {a,b,4,4} | fω3+4(n) | |
| Quadrimegation | {4M.} | {a,a,b,4} | fω4(n) | |
| Quadrimega-addition | Pentonation | {4M.1} | {a,b,1,5} | fω4+1(n) |
| Quintimegation | {5M.} | {a,a,b,5} | fω5(n) | |
| Quintimega-addition | Hexonation | {5M.1} | {a,b,1,6} | fω5+1(n) |
| Sextimegation | {6M.} | {a,a,b,6} | fω6(n) | |
| Sextimega-addition | Heptonation | {6M.1} | {a,b,1,7} | fω6+1(n) |
| Septimegation | {7M.} | {a,a,b,7} | fω7(n) | |
| Septimega-addition | Octonation | {7M.1} | {a,b,1,8} | fω7+1(n) |
| Octimegation | {8M.} | {a,a,b,8} | fω8(n) | |
| Octimega-addition | Ennonation | {8M.1} | {a,b,1,9} | fω8+1(n) |
| Nonimegation | {9M.} | {a,a,b,9} | fω9(n) | |
| Nonimega-addition | Deconation | {9M.1} | {a,b,1,10} | fω9+1(n) |
| Expomegation | {eM.} = {{1}M.} | {a,a,a,b} | fω2(n) | |
| Expomega-addition | Megotion | {eM.1} = {{1}M.1} | {a,b,1,1,2} | fω2+1(n) |
| Expomega-multiplication | Multimegotion | {eM.2} = {{1}M.2} | {a,b,2,1,2} | fω2+2(n) |
| Expomega-exponentiation | Powermegotion | {eM.3} = {{1}M.3} | {a,b,3,1,2} | fω2+3(n) |
| Expomega-tetration | Megotetration | {eM.4} = {{1}M.4} | {a,b,4,1,2} | fω2+4(n) |
| Expomega-megation | {eM.M.} = {{1}M.M.} | {a,a,b,1,2} | fω2+ω(n) | |
| Expomega-mega-addition | Megoexpansion | {eM.M.1} = {{1}M.M.1} | {a,b,1,2,2} | fω2+ω+1(n) |
| Expomega-duomegation | {eM.2M.} = {{1}M.2M.} | {a,a,b,2,2} | fω2+ω2(n) | |
| Expoduomegation | {e2M.} = {{1}2M.} | {a,a,a,b,2} | f(ω2)2(n) | |
| Expoduomega-addition | Gigotion | {e2M.1} = {{1}2M.1} | {a,b,1,1,3} | f(ω2)2+1(n) |
| Expotrimegation | {e3M.} = {{1}3M.} | {a,a,a,b,3} | f(ω2)3(n) | |
| Expotrimega-addition | Terotion | {e3M.1} = {{1}3M.1} | {a,b,1,1,4} | f(ω2)3+1(n) |
| Expoquadrimegation | {e4M.} = {{1}4M.} | {a,a,a,b,4} | f(ω2)4(n) | |
| Expoquadrimega-addition | Petotion | {e4M.1} = {{1}4M.1} | {a,b,1,1,5} | f(ω2)4+1(n) |
| Duoexpomegation | {2eM.} = {2{1}M.} | {a,a,a,a,b} | fω3(n) | |
| Duoexpomega-addition | Powiaination | {2eM.1} = {2{1}M.1} | {a,b,1,1,1,2} | fω3+1(n) |
| Duoexpoduomegation | {2e2M.} = {2{1}2M.} | {a,a,a,a,b,2} | f(ω3)2(n) | |
| Triexpomegation | {3eM.} = {3{1}M.} | {a,a,a,a,a,b} | fω4(n) | |
| Quadriexpomegation | {4eM.} = {4{1}M.} | {a,a,a,a,a,a,b} | fω5(n) | |
| Quintiexpomegation | {5eM.} = {5{1}M.} | {a,a,a,a,a,a,a,b} | fω6(n) | |
| Tetramegation | {tM.} = {{2}M.} | {a,b[2]2} | fωω(n) | |
| Tetra-by-duomegation | {t2M.} = {{2}2M.} | {a,b[2]1[2]2} | fωω2(n) | |
| Tetra-by-expomegation | {teM.} = {{2}{1}M.} | {a,b[3]2} | fωω2(n) | |
| Tetra-by-duoexpomegation | {t2eM.} = {{2}2{1}M.} | {a,b[4]2} | fωω3(n) | |
| Duotetramegation | {2tM.} = {2{2}M.} | {a,b[1,2]2} | fωωω(n) | |
| Tritetramegation | {3tM.} = {3{2}M.} | {a,b[1[2]2]2} | f4ω(n) | |
| Quadritetramegation | {4tM.} = {4{2}M.} | {a,b[1[1,2]2]2} | f5ω(n) | |
| Quintitetramegation | {5tM.} = {5{2}M.} | {a,b[1[1[2]2]2]2} | f6ω(n) | |
| The following names are from a less well-defined extension of the naming system! | ||||
| Pentamegation | {pM.} = {{3}M.} | {a,b[1\2]2} | fε0(n) | |
| Pentaduomegation | {p2M.} = {{3}2M.} | {a,b[1[1\2]2\2]2} | fε02(n) | |
| Duopentamegation | {2pM.} = {2{3}M.} | {a,b[1\1[1\2]2]2} | fεε0(n) | |
| Hexamegation | {hM.} = {{4}M.} | {a,b[1\1\2]2} | fζ0(n) | |
| Heptamegation | {{5}M.} | {a,b[1\1\1\2]2} | fη0(n) | |
| Megamegation | {{M.}M.} | {a,b[1\\2]2} | fφ(ω,0)(n) | |
| Duomegamegation | {{2M.}M.} | {a,b[1\\1\\2]2} | fφ(ω2,0)(n) | |
| Expomegamegation | {{eM.}M.} | {a,b[1[3]\2]2} | fφ(ω2,0)(n) | |
| Tetramegamegation | {{tM.}M.} | {a,b[1[1,2]\2]2} | fφ(ωω,0)(n) | |
| Pentamegamegation | {{pM.}M.} | {a,b[1[1\2]\2]2} | fφ(ε0,0)(n) | |
| Megamegamegation | {{{M.}M.}M.} | {a,b[1[1\\2]\2]2} | fφ(φ(ω,0),0)(n) | |
| Megamegamegamegation | {{{{M.}M.}M.}M.} | {a,b[1[1[1\\2]\2]\2]2} | fφ(φ(φ(ω,0),0),0)(n) | |
| Limit of naming scheme | {a,b[1/2]2} | fφ(1,0,0)(n) | ||