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The dekaelgathor regiment is a series of numbers from E100(#^#^#^10)100 to E100(#^#^#^90)100 defined using Cascading-E notation (i.e. beginning from dekaelgathor and up to enenintaelgathor).[1] The numbers were coined by Sbiis Saibian.

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## List of numbers of the regiment Edit

 Name of number Cascading-E notation (definition) Fast-growing hierarchy (approximation) dekaelgathor E100(#^#^#^10)100 $$f_{\omega^{\omega^{\omega^{10}}}}(100)$$ grand dekaelgathor E100(#^#^#^10)100#2 $$f_{\omega^{\omega^{\omega^{10}}}}^2(100)$$ grangol-carta-dekaelgathor E100(#^#^#^10)100#100 $$f_{\omega^{\omega^{\omega^{10}}}+1}(100)$$ godgahlah-carta-dekaelgathor E100(#^#^#^10)100#^#100 $$f_{\omega^{\omega^{\omega^{10}}}+\omega^{\omega}}(100)$$ godgathor-carta-dekaelgathor E100(#^#^#^10)100#^#^#100 $$f_{\omega^{\omega^{\omega^{10}}}+\omega^{\omega^{\omega}}}(100)$$ gralgathor-carta-dekaelgathor E100(#^#^#^10)100#^#^##100 $$f_{\omega^{\omega^{\omega^{10}}}+\omega^{\omega^{\omega^2}}}(100)$$ thraelgathor-carta-dekaelgathor E100(#^#^#^10)100#^#^###100 $$f_{\omega^{\omega^{\omega^{10}}}+\omega^{\omega^{\omega^3}}}(100)$$ terinngathor-carta-dekaelgathor E100(#^#^#^10)100#^#^####100 $$f_{\omega^{\omega^{\omega^{10}}}+\omega^{\omega^{\omega^4}}}(100)$$ pentaelgathor-carta-dekaelgathor E100(#^#^#^10)100(#^#^#^5)100 $$f_{\omega^{\omega^{\omega^{10}}}+\omega^{\omega^{\omega^5}}}(100)$$ hexaelgathor-carta-dekaelgathor E100(#^#^#^10)100(#^#^#^6)100 $$f_{\omega^{\omega^{\omega^{10}}}+\omega^{\omega^{\omega^6}}}(100)$$ heptaelgathor-carta-dekaelgathor E100(#^#^#^10)100(#^#^#^7)100 $$f_{\omega^{\omega^{\omega^{10}}}+\omega^{\omega^{\omega^7}}}(100)$$ octaelgathor-carta-dekaelgathor E100(#^#^#^10)100(#^#^#^8)100 $$f_{\omega^{\omega^{\omega^{10}}}+\omega^{\omega^{\omega^8}}}(100)$$ ennaelgathor-carta-dekaelgathor E100(#^#^#^10)100(#^#^#^9)100 $$f_{\omega^{\omega^{\omega^{10}}}+\omega^{\omega^{\omega^9}}}(100)$$ dekaeltrigathor E100(#^#^#^10)100(#^#^#^10)100 $$f_{\omega^{\omega^{\omega^{10}}}2}(100)$$ dekaeltergathor E100(#^#^#^10)*#4 $$f_{\omega^{\omega^{\omega^{10}}}3}(100)$$ dekaelpeggathor E100(#^#^#^10)*#5 $$f_{\omega^{\omega^{\omega^{10}}}4}(100)$$ dekaelhexgathor E100(#^#^#^10)*#6 $$f_{\omega^{\omega^{\omega^{10}}}5}(100)$$ dekaelhepgathor E100(#^#^#^10)*#7 $$f_{\omega^{\omega^{\omega^{10}}}6}(100)$$ dekael-ahtgathor E100(#^#^#^10)*#8 $$f_{\omega^{\omega^{\omega^{10}}}7}(100)$$ dekael-enngathor E100(#^#^#^10)*#9 $$f_{\omega^{\omega^{\omega^{10}}}8}(100)$$ dekaeldekagathor E100(#^#^#^10)*#10 $$f_{\omega^{\omega^{\omega^{10}}}9}(100)$$ dekaelgathor-by-hyperion E100(#^#^#^10)*#100 $$f_{\omega^{\omega^{\omega^{10}}+1}}(100)$$ dekaelgathor-by-godgahlah E100(#^#^#^10)*#^#100 $$f_{\omega^{\omega^{\omega^{10}}+\omega}}(100)$$ dekaelgathor-by-godgathor E100(#^#^#^10)*#^#^#100 $$f_{\omega^{\omega^{\omega^{10}}+\omega^{\omega}}}(100)$$ dekaelgathor-by-gralgathor E100(#^#^#^10)*#^#^##10 $$f_{\omega^{\omega^{\omega^{10}}+\omega^{\omega^2}}}(100)$$ dekaelgathor-by-thraelgathor E100(#^#^#^10)*#^#^###100 $$f_{\omega^{\omega^{\omega^{10}}+\omega^{\omega^3}}}(100)$$ dekaelgathor-by-terinngathor E100(#^#^#^10)*#^#^####100 $$f_{\omega^{\omega^{\omega^{10}}+\omega^{\omega^4}}}(100)$$ dekaelgathor-by-pentaelgathor E100(#^#^#^10)*(#^#^#^5)100 $$f_{\omega^{\omega^{\omega^{10}}+\omega^{\omega^5}}}(100)$$ dekaelgathor-by-hexaelgathor E100(#^#^#^10)*(#^#^#^6)100 $$f_{\omega^{\omega^{\omega^{10}}+\omega^{\omega^6}}}(100)$$ dekaelgathor-by-heptaelgathor E100(#^#^#^10)*(#^#^#^7)100 $$f_{\omega^{\omega^{\omega^{10}}+\omega^{\omega^7}}}(100)$$ dekaelgathor-by-octaelgathor E100(#^#^#^10)*(#^#^#^8)100 $$f_{\omega^{\omega^{\omega^{10}}+\omega^{\omega^8}}}(100)$$ dekaelgathor-by-ennaelgathor E100(#^#^#^10)*(#^#^#^9)100 $$f_{\omega^{\omega^{\omega^{10}}+\omega^{\omega^9}}}(100)$$ deutero-dekaelgathor E100(#^#^#^10)*(#^#^#^10)100 $$f_{\omega^{\omega^{\omega^{10}}2}}(100)$$ trito-dekaelgathor E100(#^#^#^10)*(#^#^#^10)*(#^#^#^10)100 $$f_{\omega^{\omega^{\omega^{10}}3}}(100)$$ teterto-dekaelgathor E100#^(#^#^10*#)4 $$f_{\omega^{\omega^{\omega^{10}}4}}(100)$$ pepto-dekaelgathor E100#^(#^#^10*#)5 $$f_{\omega^{\omega^{\omega^{10}}5}}(100)$$ exto-dekaelgathor E100#^(#^#^10*#)6 $$f_{\omega^{\omega^{\omega^{10}}6}}(100)$$ epto-dekaelgathor E100#^(#^#^10*#)7 $$f_{\omega^{\omega^{\omega^{10}}7}}(100)$$ ogdo-dekaelgathor E100#^(#^#^10*#)8 $$f_{\omega^{\omega^{\omega^{10}}8}}(100)$$ ento-dekaelgathor E100#^(#^#^10*#)9 $$f_{\omega^{\omega^{\omega^{10}}9}}(100)$$ dekato-dekaelgathor E100#^(#^#^10*#)10 $$f_{\omega^{\omega^{\omega^{10}}10}}(100)$$ isosto-dekaelgathor E100#^(#^#^10*#)20 $$f_{\omega^{\omega^{\omega^{10}}20}}(100)$$ trianto-dekaelgathor E100#^(#^#^10*#)30 $$f_{\omega^{\omega^{\omega^{10}}30}}(100)$$ saranto-dekaelgathor E100#^(#^#^10*#)40 $$f_{\omega^{\omega^{\omega^{10}}40}}(100)$$ peninto-dekaelgathor E100#^(#^#^10*#)50 $$f_{\omega^{\omega^{\omega^{10}}50}}(100)$$ exinto-dekaelgathor E100#^(#^#^10*#)60 $$f_{\omega^{\omega^{\omega^{10}}60}}(100)$$ ebdominto-dekaelgathor E100#^(#^#^10*#)70 $$f_{\omega^{\omega^{\omega^{10}}70}}(100)$$ ogdonto-dekaelgathor E100#^(#^#^10*#)80 $$f_{\omega^{\omega^{\omega^{10}}80}}(100)$$ eneninto-dekaelgathor E100#^(#^#^10*#)90 $$f_{\omega^{\omega^{\omega^{10}}90}}(100)$$ hecato-dekaelgathor E100#^(#^#^10*#)100 $$f_{\omega^{\omega^{\omega^{10}+1}}}(100)$$ dekaelgridgathor E100#^(#^#^10*##)100 $$f_{\omega^{\omega^{\omega^{10}+2}}}(100)$$ dekaelkubikgathor E100#^(#^#^10*###)100 $$f_{\omega^{\omega^{\omega^{10}+3}}}(100)$$ dekaelquarticgathor E100#^(#^#^10*####)100 $$f_{\omega^{\omega^{\omega^{10}+4}}}(100)$$ dekaelgodgathgathor E100#^(#^#^10*#^#)100 $$f_{\omega^{\omega^{\omega^{10}+\omega}}}(100)$$ dekaelgralgathgathor E100#^(#^#^10*#^##)100 $$f_{\omega^{\omega^{\omega^{10}+\omega^2}}}(100)$$ dekaelthraelgathgathor E100#^(#^#^10*#^###)100 $$f_{\omega^{\omega^{\omega^{10}+\omega^3}}}(100)$$ dekaelterinngathgathor E100#^(#^#^10*#^####)100 $$f_{\omega^{\omega^{\omega^{10}+\omega^4}}}(100)$$ dekaelpentaelgathgathor E100#^(#^#^10*#^#^5)100 $$f_{\omega^{\omega^{\omega^{10}+\omega^5}}}(100)$$ dekaelhexaelgathgathor E100#^(#^#^10*#^#^6)100 $$f_{\omega^{\omega^{\omega^{10}+\omega^6}}}(100)$$ dekaelheptaelgathgathor E100#^(#^#^10*#^#^7)100 $$f_{\omega^{\omega^{\omega^{10}+\omega^7}}}(100)$$ dekaeloctaelgathgathor E100#^(#^#^10*#^#^8)100 $$f_{\omega^{\omega^{\omega^{10}+\omega^8}}}(100)$$ dekaelennaelgathgathor E100#^(#^#^10*#^#^9)100 $$f_{\omega^{\omega^{\omega^{10}+\omega^9}}}(100)$$ dekaelgathordeus E100#^(#^#^10*#^#^10)100 $$f_{\omega^{\omega^{\omega^{10}2}}}(100)$$ dekaelgathortruce E100#^(#^#^10*#^#^10*#^#^10)100 $$f_{\omega^{\omega^{\omega^{10}3}}}(100)$$ dekaelgathorquad E100(#^#^#^11)4 $$f_{\omega^{\omega^{\omega^{10}4}}}(100)$$ dekaelgathorquid E100(#^#^#^11)5 $$f_{\omega^{\omega^{\omega^{10}5}}}(100)$$ dekaelgathorsid E100(#^#^#^11)6 $$f_{\omega^{\omega^{\omega^{10}6}}}(100)$$ dekaelgathorseptuce E100(#^#^#^11)7 $$f_{\omega^{\omega^{\omega^{10}7}}}(100)$$ dekaelgathoroctuce E100(#^#^#^11)8 $$f_{\omega^{\omega^{\omega^{10}8}}}(100)$$ dekaelgathornonice E100(#^#^#^11)9 $$f_{\omega^{\omega^{\omega^{10}9}}}(100)$$ dekaelgathordecice E100(#^#^#^11)10 $$f_{\omega^{\omega^{\omega^{10}10}}}(100)$$ dekaelgathorvigintice E100(#^#^#^11)20 $$f_{\omega^{\omega^{\omega^{10}20}}}(100)$$ dekaelgathortrigintice E100(#^#^#^11)30 $$f_{\omega^{\omega^{\omega^{10}30}}}(100)$$ dekaelgathorquadragintice E100(#^#^#^11)40 $$f_{\omega^{\omega^{\omega^{10}40}}}(100)$$ dekaelgathorquinquagintice E100(#^#^#^11)50 $$f_{\omega^{\omega^{\omega^{10}50}}}(100)$$ dekaelgathorsexagintice E100(#^#^#^11)60 $$f_{\omega^{\omega^{\omega^{10}60}}}(100)$$ dekaelgathorseptuagintice E100(#^#^#^11)70 $$f_{\omega^{\omega^{\omega^{10}70}}}(100)$$ dekaelgathoroctogintice E100(#^#^#^11)80 $$f_{\omega^{\omega^{\omega^{10}80}}}(100)$$ dekaelgathornonagintice E100(#^#^#^11)90 $$f_{\omega^{\omega^{\omega^{10}90}}}(100)$$ endekaelgathor E100(#^#^#^11)100 $$f_{\omega^{\omega^{\omega^{11}}}}(100)$$ dodekaelgathor E100(#^#^#^12)100 $$f_{\omega^{\omega^{\omega^{12}}}}(100)$$ triadekaelgathor E100(#^#^#^13)100 $$f_{\omega^{\omega^{\omega^{13}}}}(100)$$ tetradekaelgathor E100(#^#^#^14)100 $$f_{\omega^{\omega^{\omega^{14}}}}(100)$$ pentadekaelgathor E100(#^#^#^15)100 $$f_{\omega^{\omega^{\omega^{15}}}}(100)$$ hexadekaelgathor E100(#^#^#^16)100 $$f_{\omega^{\omega^{\omega^{16}}}}(100)$$ heptadekaelgathor E100(#^#^#^17)100 $$f_{\omega^{\omega^{\omega^{17}}}}(100)$$ octadekaelgathor E100(#^#^#^18)100 $$f_{\omega^{\omega^{\omega^{18}}}}(100)$$ ennadekaelgathor E100(#^#^#^19)100 $$f_{\omega^{\omega^{\omega^{19}}}}(100)$$ icosi-aelgathor E100(#^#^#^20)100 $$f_{\omega^{\omega^{\omega^{20}}}}(100)$$ triantaelgathor E100(#^#^#^30)100 $$f_{\omega^{\omega^{\omega^{30}}}}(100)$$ sarantaelgathor E100(#^#^#^40)100 $$f_{\omega^{\omega^{\omega^{40}}}}(100)$$ penintaelgathor E100(#^#^#^50)100 $$f_{\omega^{\omega^{\omega^{50}}}}(100)$$ exintaelgathor E100(#^#^#^60)100 $$f_{\omega^{\omega^{\omega^{60}}}}(100)$$ ebdomintaelgathor E100(#^#^#^70)100 $$f_{\omega^{\omega^{\omega^{70}}}}(100)$$ ogdontaelgathor E100(#^#^#^80)100 $$f_{\omega^{\omega^{\omega^{80}}}}(100)$$ enenintaelgathor E100(#^#^#^90)100 $$f_{\omega^{\omega^{\omega^{90}}}}(100)$$

## Sources Edit

1. Saibian, Sbiis. Cascading-E Numbers. Retrieved 2017-10-13.