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

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## List of numbers of the regiment

 Name of number Cascading-E notation (definition) Fast-growing hierarchy (approximation) Thraelgathor E100#^#^###100 $$f_{\omega^{\omega^{\omega^3}}}(100)$$ Grand thraelgathor E100#^#^###100#2 $$f_{\omega^{\omega^{\omega^3}}}^2(100)$$ Grangol-carta-thraelgathor E100#^#^###100#100 $$f_{\omega^{\omega^{\omega^3}}+1}(100)$$ Gugold-carta-thraelgathor E100#^#^###100##100 $$f_{\omega^{\omega^{\omega^3}}+\omega}(100)$$ Throogol-carta-thraelgathor E100#^#^###100###100 $$f_{\omega^{\omega^{\omega^3}}+\omega^2}(100)$$ Tetroogol-carta-thraelgathor E100#^#^###100####100 $$f_{\omega^{\omega^{\omega^3}}+\omega^3}(100)$$ Godgahlah-carta-thraelgathor E100#^#^###100#^#100 $$f_{\omega^{\omega^{\omega^3}}+\omega^\omega}(100)$$ Gridgahlah-carta-thraelgathor E100#^#^###100#^##100 $$f_{\omega^{\omega^{\omega^3}}+\omega^{\omega^2}}(100)$$ Kubikahlah-carta-thraelgathor E100#^#^###100#^###100 $$f_{\omega^{\omega^{\omega^3}}+\omega^{\omega^3}}(100)$$ Quarticahlah-carta-thraelgathor E100#^#^###100#^####100 $$f_{\omega^{\omega^{\omega^3}}+\omega^{\omega^4}}(100)$$ Godgathor-carta-thraelgathor E100#^#^###100#^#^#100 $$f_{\omega^{\omega^{\omega^3}}+\omega^{\omega^\omega}}(100)$$ Gralgathor-carta-thraelgathor E100#^#^###100#^#^##100 $$f_{\omega^{\omega^{\omega^3}}+\omega^{\omega^{\omega^2}}}(100)$$ Thraeltrigathor E100#^#^###100#^#^###100 $$f_{\omega^{\omega^{\omega^3}}2}(100)$$ Thraeltergathor E100#^#^###100#^#^###100#^#^###100 = E100#^#^###*#4 $$f_{\omega^{\omega^{\omega^3}}3}(100)$$ Thraelpeggathor E100#^#^###*#5 $$f_{\omega^{\omega^{\omega^3}}4}(100)$$ Thraelhexgathor E100#^#^###*#6 $$f_{\omega^{\omega^{\omega^3}}5}(100)$$ Thraelhepgathor E100#^#^###*#7 $$f_{\omega^{\omega^{\omega^3}}6}(100)$$ Thrael-ahtgathor E100#^#^###*#8 $$f_{\omega^{\omega^{\omega^3}}7}(100)$$ Thrael-enngathor E100#^#^###*#9 $$f_{\omega^{\omega^{\omega^3}}8}(100)$$ Thraeldekagathor E100#^#^###*#10 $$f_{\omega^{\omega^{\omega^3}}9}(100)$$ Deutero-thraelgathor E100#^#^###*#^#^###100 $$f_{\omega^{\omega^{\omega^3}2}}(100)$$ Trito-thraelgathor E100#^#^###*#^#^###*#^#^###100 $$f_{\omega^{\omega^{\omega^3}3}}(100)$$ Teterto-thraelgathor E100#^#^###*#^#^###*#^#^###*#^#^###100 = E100#^(#^###*#)4 $$f_{\omega^{\omega^{\omega^3}4}}(100)$$ Pepto-thraelgathor E100#^(#^###*#)5 $$f_{\omega^{\omega^{\omega^3}5}}(100)$$ Exto-thraelgathor E100#^(#^###*#)6 $$f_{\omega^{\omega^{\omega^3}6}}(100)$$ Epto-thraelgathor E100#^(#^###*#)7 $$f_{\omega^{\omega^{\omega^3}7}}(100)$$ Ogdo-thraelgathor E100#^(#^###*#)8 $$f_{\omega^{\omega^{\omega^3}8}}(100)$$ Ento-thraelgathor E100#^(#^###*#)9 $$f_{\omega^{\omega^{\omega^3}9}}(100)$$ Dekato-thraelgathor E100#^(#^###*#)10 $$f_{\omega^{\omega^{\omega^3}10}}(100)$$ Isosto-thraelgathor E100#^(#^###*#)20 $$f_{\omega^{\omega^{\omega^3}20}}(100)$$ Trianto-thraelgathor E100#^(#^###*#)30 $$f_{\omega^{\omega^{\omega^3}30}}(100)$$ Saranto-thraelgathor E100#^(#^###*#)40 $$f_{\omega^{\omega^{\omega^3}40}}(100)$$ Peninto-thraelgathor E100#^(#^###*#)50 $$f_{\omega^{\omega^{\omega^3}50}}(100)$$ Exinto-thraelgathor E100#^(#^###*#)60 $$f_{\omega^{\omega^{\omega^3}60}}(100)$$ Ebdominto-thraelgathor E100#^(#^###*#)70 $$f_{\omega^{\omega^{\omega^3}70}}(100)$$ Ogdonto-thraelgathor E100#^(#^###*#)80 $$f_{\omega^{\omega^{\omega^3}80}}(100)$$ Eneninto-thraelgathor E100#^(#^###*#)90 $$f_{\omega^{\omega^{\omega^3}90}}(100)$$ Hecato-thraelgathor E100#^(#^###*#)100 $$f_{\omega^{\omega^{\omega^3+1}}}(100)$$ Thraelgridgathor E100#^(#^###*##)100 $$f_{\omega^{\omega^{\omega^3+2}}}(100)$$ Thraelkubikgathor E100#^(#^###*###)100 $$f_{\omega^{\omega^{\omega^3+3}}}(100)$$ Thraelquarticgathor E100#^(#^###*####)100 $$f_{\omega^{\omega^{\omega^3+4}}}(100)$$ Thraelgodgathgathor E100#^(#^###*#^#)100 $$f_{\omega^{\omega^{\omega^3+\omega}}}(100)$$ Thraelgodgathordeusgathor E100#^(#^###*#^#*#^#)100 $$f_{\omega^{\omega^{\omega^3+\omega2}}}(100)$$ Thraelgodgathortrucegathor E100#^(#^###*#^#*#^#*#^#)100 $$f_{\omega^{\omega^{\omega^3+\omega3}}}(100)$$ Thraelgodgathorquadgathor E100#^(#^###*#^#*#^#*#^#*#^#)100 = E100#^(#^###*#^##)4 $$f_{\omega^{\omega^{\omega^3+\omega4}}}(100)$$ Thraelgodgathorquidgathor E100#^(#^###*#^##)5 $$f_{\omega^{\omega^{\omega^3+\omega5}}}(100)$$ Thraelgodgathorsidgathor E100#^(#^###*#^##)6 $$f_{\omega^{\omega^{\omega^3+\omega6}}}(100)$$ Thraelgodgathorseptucegathor E100#^(#^###*#^##)7 $$f_{\omega^{\omega^{\omega^3+\omega7}}}(100)$$ Thraelgodgathoroctucegathor E100#^(#^###*#^##)8 $$f_{\omega^{\omega^{\omega^3+\omega8}}}(100)$$ Thraelgodgathornonicegathor E100#^(#^###*#^##)9 $$f_{\omega^{\omega^{\omega^3+\omega9}}}(100)$$ Thraelgodgathordecicegathor E100#^(#^###*#^##)10 $$f_{\omega^{\omega^{\omega^3+\omega10}}}(100)$$ Thraelgodgathorviginticegathor E100#^(#^###*#^##)20 $$f_{\omega^{\omega^{\omega^3+\omega20}}}(100)$$ Thraelgodgathorquinquaginticegathor E100#^(#^###*#^##)50 $$f_{\omega^{\omega^{\omega^3+\omega50}}}(100)$$ Thraelgralgathgathor E100#^(#^###*#^##)100 $$f_{\omega^{\omega^{\omega^3+\omega^2}}}(100)$$ Thraelgralgodgathgathgathor E100#^(#^###*#^##*#^#)100 $$f_{\omega^{\omega^{\omega^3+\omega^2+\omega}}}(100)$$ Thraelgralgodgathordeusgathgathor E100#^(#^###*#^##*#^#*#^#)100 $$f_{\omega^{\omega^{\omega^3+\omega^2+\omega2}}}(100)$$ Thraelgralgathordeusgathor E100#^(#^###*#^##*#^##)100 $$f_{\omega^{\omega^{\omega^3+\omega^22}}}(100)$$ Thraelgralgathortrucegathor E100#^(#^###*#^##*#^##*#^##)100 $$f_{\omega^{\omega^{\omega^3+\omega^23}}}(100)$$ Thraelgralgathorquadgathor E100#^(#^###*#^##*#^##*#^##*#^##)100 = E100#^(#^###*#^###)4 $$f_{\omega^{\omega^{\omega^3+\omega^24}}}(100)$$ Thraelgralgathorquidgathor E100#^(#^###*#^###)5 $$f_{\omega^{\omega^{\omega^3+\omega^25}}}(100)$$ Thraelgralgathorsidgathor E100#^(#^###*#^###)6 $$f_{\omega^{\omega^{\omega^3+\omega^26}}}(100)$$ Thraelgralgathorseptucegathor E100#^(#^###*#^###)7 $$f_{\omega^{\omega^{\omega^3+\omega^27}}}(100)$$ Thraelgralgathoroctucegathor E100#^(#^###*#^###)8 $$f_{\omega^{\omega^{\omega^3+\omega^28}}}(100)$$ Thraelgralgathornonicegathor E100#^(#^###*#^###)9 $$f_{\omega^{\omega^{\omega^3+\omega^29}}}(100)$$ Thraelgralgathordecicegathor E100#^(#^###*#^###)10 $$f_{\omega^{\omega^{\omega^3+\omega^210}}}(100)$$ Thraelgralgathorviginticegathor E100#^(#^###*#^###)20 $$f_{\omega^{\omega^{\omega^3+\omega^220}}}(100)$$ Thraelgralgathorquinquaginticegathor E100#^(#^###*#^###)50 $$f_{\omega^{\omega^{\omega^3+\omega^250}}}(100)$$ Thraelgathordeus E100#^(#^###*#^###)100 $$f_{\omega^{\omega^{\omega^32}}}(100)$$ Thraelgodgathgathordeus E100#^(#^###*#^###*#^#)100 $$f_{\omega^{\omega^{\omega^32+\omega}}}(100)$$ Thraelgralgathgathordeus E100#^(#^###*#^###*#^##)100 $$f_{\omega^{\omega^{\omega^32+\omega^2}}}(100)$$ Thraelgathortruce E100#^(#^###*#^###*#^###)100 $$f_{\omega^{\omega^{\omega^33}}}(100)$$ Thraelgathorquad E100#^(#^###*#^###*#^###*#^###)100 = E100#^#^####4 $$f_{\omega^{\omega^{\omega^34}}}(100)$$ Thraelgathorquid E100#^#^####5 $$f_{\omega^{\omega^{\omega^35}}}(100)$$ Thraelgathorsid E100#^#^####6 $$f_{\omega^{\omega^{\omega^36}}}(100)$$ Thraelgathorseptuce E100#^#^####7 $$f_{\omega^{\omega^{\omega^37}}}(100)$$ Thraelgathoroctuce E100#^#^####8 $$f_{\omega^{\omega^{\omega^38}}}(100)$$ Thraelgathornonice E100#^#^####9 $$f_{\omega^{\omega^{\omega^39}}}(100)$$ Thraelgathordecice E100#^#^####10 $$f_{\omega^{\omega^{\omega^310}}}(100)$$ Thraelgathorvigintice E100#^#^####20 $$f_{\omega^{\omega^{\omega^320}}}(100)$$ Thraelgathortrigintice E100#^#^####30 $$f_{\omega^{\omega^{\omega^330}}}(100)$$ Thraelgathorquadragintice E100#^#^####40 $$f_{\omega^{\omega^{\omega^340}}}(100)$$ Thraelgathorquinquagintice E100#^#^####50 $$f_{\omega^{\omega^{\omega^350}}}(100)$$ Thraelgathorsexagintice E100#^#^####60 $$f_{\omega^{\omega^{\omega^360}}}(100)$$ Thraelgathorseptuagintice E100#^#^####70 $$f_{\omega^{\omega^{\omega^370}}}(100)$$ Thraelgathoroctogintice E100#^#^####80 $$f_{\omega^{\omega^{\omega^380}}}(100)$$ Thraelgathornonagintice E100#^#^####90 $$f_{\omega^{\omega^{\omega^390}}}(100)$$

## Sources

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