Thraelgathor regiment

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). The numbers were coined by Sbiis Saibian.
Previous regiment 	Next regiment
Gralgathor regiment	Terinngathor regiment
== 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 ==
Category:Numbers
Category:Numbers by Sbiis Saibian
Category:Double exponentiated polynomial omega level
Category:Saibian's regiments
Category:Series
Category:Cascading-E numbers