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The gralgathor regiment is a series of numbers from E100#^#^##100 to E100#^#^###90 defined using Cascading-E notation (i.e. beginning from gralgathor and up to gralgathornonagintice).[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) gralgathor E100#^#^##100 = $$f_{\omega^{\omega^{\omega^2}}}(100)$$ grand gralgathor E100#^#^##100#2 $$f_{\omega^{\omega^{\omega^2}}}^2(100)$$ grangol-carta-gralgathor E100#^#^##100#100 $$f_{\omega^{\omega^{\omega^2}}+1}(100)$$ gugold-carta-gralgathor E100#^#^##100##100 $$f_{\omega^{\omega^{\omega^2}}+\omega}(100)$$ throogol-carta-gralgathor E100#^#^##100###100 $$f_{\omega^{\omega^{\omega^2}}+\omega^2}(100)$$ tetroogol-carta-gralgathor E100#^#^##100####100 $$f_{\omega^{\omega^{\omega^2}}+\omega^3}(100)$$ godgahlah-carta-gralgathor E100#^#^##100#^#100 $$f_{\omega^{\omega^{\omega^2}}+\omega^\omega}(100)$$ gridgahlah-carta-gralgathor E100#^#^##100#^##100 $$f_{\omega^{\omega^{\omega^2}}+\omega^{\omega^2}}(100)$$ kubikahlah-carta-gralgathor E100#^#^##100#^###100 $$f_{\omega^{\omega^{\omega^2}}+\omega^{\omega^3}}(100)$$ quarticahlah-carta-gralgathor E100#^#^##100#^####100 $$f_{\omega^{\omega^{\omega^2}}+\omega^{\omega^4}}(100)$$ godgathor-carta-gralgathor E100#^#^##100#^#^#100 $$f_{\omega^{\omega^{\omega^2}}+\omega^{\omega^\omega}}(100)$$ graltrigathor E100#^#^##100#^#^##100 $$f_{\omega^{\omega^{\omega^2}}2}(100)$$ graltergathor E100#^#^##100#^#^##100#^#^##100 $$f_{\omega^{\omega^{\omega^2}}3}(100)$$ deutero-gralgathor E100#^#^##*#^#^##100 $$f_{\omega^{\omega^{\omega^2}2}}(100)$$ trito-gralgathor E100#^#^##*#^#^##*#^#^##100 $$f_{\omega^{\omega^{\omega^2}3}}(100)$$ teterto-gralgathor E100#^(#^##*#)4 $$f_{\omega^{\omega^{\omega^2}4}}(100)$$ pepto-gralgathor E100#^(#^##*#)5 $$f_{\omega^{\omega^{\omega^2}5}}(100)$$ exto-gralgathor E100#^(#^##*#)6 $$f_{\omega^{\omega^{\omega^2}6}}(100)$$ epto-gralgathor E100#^(#^##*#)7 $$f_{\omega^{\omega^{\omega^2}7}}(100)$$ ogdo-gralgathor E100#^(#^##*#)8 $$f_{\omega^{\omega^{\omega^2}8}}(100)$$ ento-gralgathor E100#^(#^##*#)9 $$f_{\omega^{\omega^{\omega^2}9}}(100)$$ dekato-gralgathor E100#^(#^##*#)10 $$f_{\omega^{\omega^{\omega^2}10}}(100)$$ isosto-gralgathor E100#^(#^##*#)20 $$f_{\omega^{\omega^{\omega^2}20}}(100)$$ trianto-gralgathor E100#^(#^##*#)30 $$f_{\omega^{\omega^{\omega^2}30}}(100)$$ saranto-gralgathor E100#^(#^##*#)40 $$f_{\omega^{\omega^{\omega^2}40}}(100)$$ peninto-gralgathor E100#^(#^##*#)50 $$f_{\omega^{\omega^{\omega^2}50}}(100)$$ exinto-gralgathor E100#^(#^##*#)60 $$f_{\omega^{\omega^{\omega^2}60}}(100)$$ ebdominto-gralgathor E100#^(#^##*#)70 $$f_{\omega^{\omega^{\omega^2}70}}(100)$$ ogdonto-gralgathor E100#^(#^##*#)80 $$f_{\omega^{\omega^{\omega^2}80}}(100)$$ eneninto-gralgathor E100#^(#^##*#)90 $$f_{\omega^{\omega^{\omega^2}90}}(100)$$ hecato-gralgathor E100#^(#^##*#)100 $$f_{\omega^{\omega^{\omega^2+1}}}(100)$$ gralgridgathor E100#^(#^##*##)100 $$f_{\omega^{\omega^{\omega^2+2}}}(100)$$ gralkubikgathor E100#^(#^##*###)100 $$f_{\omega^{\omega^{\omega^2+3}}}(100)$$ gralquarticgathor E100#^(#^##*####)100 $$f_{\omega^{\omega^{\omega^2+4}}}(100)$$ gralgodgathgathor E100#^(#^##*#^#)100 $$f_{\omega^{\omega^{\omega^2+\omega}}}(100)$$ gralgodgathordeusgathor E100#^(#^##*#^#*#^#)100 $$f_{\omega^{\omega^{\omega^2+\omega2}}}(100)$$ gralgodgathortrucegathor E100#^(#^##*#^#*#^#*#^#)100 $$f_{\omega^{\omega^{\omega^2+\omega3}}}(100)$$ gralgodgathorquadgathor E100#^(#^##*#^#*#^#*#^#*#^#)100 $$f_{\omega^{\omega^{\omega^2+\omega4}}}(100)$$ gralgodgathorquidgathor E100#^(#^##*#^##)5 $$f_{\omega^{\omega^{\omega^2+\omega5}}}(100)$$ gralgodgathorsidgathor E100#^(#^##*#^##)6 $$f_{\omega^{\omega^{\omega^2+\omega6}}}(100)$$ gralgodgathorseptucegathor E100#^(#^##*#^##)7 $$f_{\omega^{\omega^{\omega^2+\omega7}}}(100)$$ gralgodgathoroctucegathor E100#^(#^##*#^##)8 $$f_{\omega^{\omega^{\omega^2+\omega8}}}(100)$$ gralgodgathornonicegathor E100#^(#^##*#^##)9 $$f_{\omega^{\omega^{\omega^2+\omega9}}}(100)$$ gralgodgathordecicegathor E100#^(#^##*#^##)10 $$f_{\omega^{\omega^{\omega^2+\omega10}}}(100)$$ gralgodgathorviginticegathor E100#^(#^##*#^##)20 $$f_{\omega^{\omega^{\omega^2+\omega20}}}(100)$$ gralgodgathorquinquaginticegathor E100#^(#^##*#^##)50 $$f_{\omega^{\omega^{\omega^2+\omega50}}}(100)$$ gralgathordeus E100#^(#^##*#^##)100 = E100#^#^###2 $$f_{\omega^{\omega^{\omega^22}}}(100)$$ gralgathortruce E100#^(#^##*#^##*#^##)100 = E100#^#^###3 $$f_{\omega^{\omega^{\omega^23}}}(100)$$ gralgathorquad E100#^#^###4 $$f_{\omega^{\omega^{\omega^24}}}(100)$$ gralgathorquid E100#^#^###5 $$f_{\omega^{\omega^{\omega^25}}}(100)$$ gralgathorsid E100#^#^###6 $$f_{\omega^{\omega^{\omega^26}}}(100)$$ gralgathorseptuce E100#^#^###7 $$f_{\omega^{\omega^{\omega^27}}}(100)$$ gralgathoroctuce E100#^#^###8 $$f_{\omega^{\omega^{\omega^28}}}(100)$$ gralgathornonice E100#^#^###9 $$f_{\omega^{\omega^{\omega^29}}}(100)$$ gralgathordecice E100#^#^###10 $$f_{\omega^{\omega^{\omega^210}}}(100)$$ gralgathorvigintice E100#^#^###20 $$f_{\omega^{\omega^{\omega^220}}}(100)$$ gralgathortrigintice E100#^#^###30 $$f_{\omega^{\omega^{\omega^230}}}(100)$$ gralgathorquadragintice E100#^#^###40 $$f_{\omega^{\omega^{\omega^240}}}(100)$$ gralgathorquinquagintice E100#^#^###50 $$f_{\omega^{\omega^{\omega^250}}}(100)$$ gralgathorsexagintice E100#^#^###60 $$f_{\omega^{\omega^{\omega^260}}}(100)$$ gralgathorseptuagintice E100#^#^###70 $$f_{\omega^{\omega^{\omega^270}}}(100)$$ gralgathoroctogintice E100#^#^###80 $$f_{\omega^{\omega^{\omega^280}}}(100)$$ gralgathornonagintice E100#^#^###90 $$f_{\omega^{\omega^{\omega^290}}}(100)$$

## Sources

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