With the first milestone of the Collapsing-E notation beyond blasphemorgulus:
(325) tweilasphemorgue = E100(#{&}#){&}#100
*also called (322) blasphemorgultaxihecatontakisated-blasphemorgulus
and (326) blasphemous blasphemorgulus
This expands:
E100(#{&}#){(#{&}#){(#{&}#){(#{&}#) ... (#{&}#){(#{&}#){(#{&}#){#{&}#}#}#}# ... #}#}#}#100
w/ 100 #{&}#'s
*Saibian's and Aarex's are defined as:
E100(#{&}#){(#{&}#){(#{&}#) ... (#{&}#){(#{&}#){(#{&}#)}(#{&}#)}(#{&}#) ...(#{&}#)}(#{&}#)}(#{&}#)
w/ 100 #{&}#'s centered out
w/ 199 #{&}# total
We can continue to coin new numbers after this milestone, such as:
(327) tweilasphemorgiagong = E100,000(#{&}#){&}#100,000
...
(328) grand tweilasphemorgue = E100(#{&}#){&}#100#2
...
(329) grantweilasphemorgue = E100(#{&}#){&}#100#100
(330) gugoldtweilasphemorgue = E100(#{&}#){&}#100##100
(331) godgah-tweilasphemorgue = E100(#{&}#){&}#100#^#100
(332) tethrathoth-carta-tweilasphemorgue = E100(#{&}#){&}#100#^^#100
(333) tethracross-carta-tweilasphemorgue = E100(#{&}#){&}#100#^^##100
(334) pentacthulhum-carta-tweilasphemorgue = E100(#{&}#){&}#100#^^^#100
(335) godsgodgulus-carta-tweilasphemorgue = E100(#{&}#){&}#100#{#}#100
(336) blasphemorgulus-carta-tweilasphemorgue = E100(#{&}#){&}#100#{&}#100
(337) blasphemorgulnumus-blasphemorgulus-carta-tweilasphemorgue = E100(#{&}#){&}#100(#{&}#){#{&}#}#100
...
(338) tweilasphemorgulatri = E100(#{&}#){&}#100(#{&}#){&}#100
(339) tweilasphemorgulatet = E100(#{&}#){&}#100(#{&}#){&}#100(#{&}#){&}#100
...
(340) tweilasphemorgulus-by-hyperion = E100(#{&}#){&}#*#100
(341) tweilasphemorgulus-by-godgahlah = E100(#{&}#){&}#*#^#100
(342) tweilasphemorgulus-by-tethrathoth = E100(#{&}#){&}#*#^^#100
(343) tweilasphemorgulus-by-tethracross = E100(#{&}#){&}#*#^^##100
(344) tweilasphemorgulus-by-pentacthulhum = E100(#{&}#){&}#*#^^^#100
(345) tweilasphemorgulus-by-godsgodgulus = E100(#{&}#){&}#*#{#}#100
(346) tweilasphemorgulus-by-blasphemorgulus = E100(#{&}#){&}#*#{&}#100
(347) tweilasphemorgulus-by-blasphemorgulnumus-blasphemorgulus = E100(#{&}#){&}#*(#{&}#){#{&}#}#100
...
(348) deutero-tweilasphemorgue = E100(#{&}#){&}#*(#{&}#){&}#100
(349) trito-tweilasphemorgue = E100(#{&}#){&}#*(#{&}#){&}#*(#{&}#){&}#100
...
(350) tweilasphemorgulfact = E100((#{&}#){&}#)^#100
(351) tweilasphemorgulus-ipso-tethrathoth = E100((#{&}#){&}#)^#^^#100
(352) tweilasphemorgulus-ipso-blasphemorgulus = E100((#{&}#){&}#)^#{&}#100
...
(353) dutetrated-tweilasphemorgulus = E100((#{&}#){&}#)^((#{&}#){&}#)100
(354) tritetrated-tweilasphemorgulus = E100((#{&}#){&}#)^((#{&}#){&}#)^((#{&}#){&}#)100
...
(355) terrible tweilasphemorgulus = E100((#{&}#){&}#)^^#100
(356) terrisquared tweilasphemorgulus = E100((#{&}#){&}#)^^##100
(357) territoped tweilasphemorgulus = E100((#{&}#){&}#)^^#^#100
(358) tethrathothi-tetrated tweilasphemorgulus = E100((#{&}#){&}#)^^#^^#100
(359) dupentated-tweilasphemorgulus = E100((#{&}#){&}#)^^((#{&}#){&}#)100
(360) tripentated-tweilasphemorgulus = E100((#{&}#){&}#)^^((#{&}#){&}#)^^((#{&}#){&}#)100
...
(361) horrible tweilasphemorgulus = E100((#{&}#){&}#)^^^#100
(362) horrendous tweilasphemorgulus = E100((#{&}#){&}#)^^^^#100
...
(363) grievous tweilasphemorgulus = E100((#{&}#){&}#){#}#100
(364) godsgodgul-centurionumus tweilasphemorgulus = E100((#{&}#){&}#){#{#}#}#100
...
(365) blasphemorgulnumus tweilasphemorgulus = E100((#{&}#){&}#){#{&}#}#100
(366) blasphemorgultaxidisated-tweilasphemorgulus = E100((#{&}#){&}#){(#{&}#){#{&}#}#}#100
...
(367) tweilasphemorgulnumus tweilasphemorgulus = E100((#{&}#){&}#){(#{&}#){&}#}#100
(368) tweilasphemorgultaxitrisated-tweilasphemorgulus = E100((#{&}#){&}#){((#{&}#){&}#){(#{&}#){&}#}#}#100
(369) tweilasphemorgultetrakisated-tweilasphemorgulus = E100((#{&}#){&}#){((#{&}#){&}#){((#{&}#){&}#){(#{&}#){&}#}#}#}#100
...
Moving on:
(370) frielasphemorgue = E100((#{&}#){&}#){&}#100
= E100((#{&}#){&}#){((#{&}#){&}#){((#{&}#){&}#){...((#{&}#){&}#){(#{&}#){(#{&}#){&}#}#}#...}#}#}#100
w/ 100 (#{&}#){&}#'s
(371) granfrielasphemorgue = E100((#{&}#){&}#){&}#100#100
(372) frielasphemorgulatri = E100((#{&}#){&}#){&}#100((#{&}#){&}#){&}#100
(373) frielasphemorgulue-by-hyperion = E100((#{&}#){&}#){&}#*#100
(374) deutero-frielasphemorgue = E100((#{&}#){&}#){&}#*((#{&}#){&}#){&}#100
(375) frielasphemorgulfact = E100(((#{&}#){&}#){&}#)^#100
(376) dutetrated-frielasphemorgue = E100(((#{&}#){&}#){&}#)^(((#{&}#){&}#){&}#)100
...
(377) terrible frielasphemorgulue = E100(((#{&}#){&}#){&}#)^^#100
(378) terrisquared frielasphemorgulue = E100(((#{&}#){&}#){&}#)^^##100
(379) horrible frielasphemorgulue = E100(((#{&}#){&}#){&}#)^^^#100
(380) horrendous frielasphemorgulue = E100(((#{&}#){&}#){&}#)^^^^#100
(381) grievous frielasphemorgulue = E100(((#{&}#){&}#){&}#){#}#100
(382) blasphemorgulnumus frielasphemorgulue = E100(((#{&}#){&}#){&}#){#{&}#}#100
(383) tweilasphemorgulnumus frielasphemorgulue = E100(((#{&}#){&}#){&}#){(#{&}#){&}#}#100
(384) frielasphemorgulnumus frielasphemorgulue = E100(((#{&}#){&}#){&}#){((#{&}#){&}#){&}#}#100
(385) frielasphemorgultaxitrisated-frielasphemorgulue = E100(((#{&}#){&}#){&}#){(((#{&}#){&}#){&}#){((#{&}#){&}#){&}#}#}#100
...
(386) fiorilasphemorgue = E100(((#{&}#){&}#){&}#){&}#100
(387) terrible fiorilasphemorgue = E100((((#{&}#){&}#){&}#){&}#)^^#100
(388) horrible fiorilasphemorgue = E100((((#{&}#){&}#){&}#){&}#)^^^#100
(389) grievous fiorilasphemorgue = E100((((#{&}#){&}#){&}#){&}#){#}#100
(390) blasphemorgulnumus fiorilasphemorgue = E100((((#{&}#){&}#){&}#){&}#){#{&}#}#100
(391) fiorilasphemorgulnumus fiorilasphemorgue = E100((((#{&}#){&}#){&}#){&}#){(((#{&}#){&}#){&}#){&}#}#100
...
(392) finnasphemorgue = E100((((#{&}#){&}#){&}#){&}#){&}#100 = E100#{&}#>#5
(393) finnasphemorgulnumus finnasphemorgue = E100(((((#{&}#){&}#){&}#){&}#){&}#){((((#{&}#){&}#){&}#){&}#){&}#}#100
...
(394) sexasphemorgue = E100(((((#{&}#){&}#){&}#){&}#){&}#){&}#100 = E100#{&}#>#6
(395) sjournalasphemorgue = E100((((((#{&}#){&}#){&}#){&}#){&}#){&}#){&}#100 = E100#{&}#>#7
(396) attalasphemorgue = E100(((((((#{&}#){&}#){&}#){&}#){&}#){&}#){&}#){&}#100 = E100#{&}#>#8
(397) neiulasphemorgue = E100((((((((#{&}#){&}#){&}#){&}#){&}#){&}#){&}#){&}#){&}#100 = E100#{&}#>#9
(398) tenasphemorgue = E100(((((((((#{&}#){&}#){&}#){&}#){&}#){&}#){&}#){&}#){&}#){&}#100 = E100#{&}#>#10
(399) elevenasphemorgue = E100#{&}#>#11
(400) twelvasphemorgue = E100#{&}#>#12
(401) thirteenasphemorgue = E100#{&}#>#13
(402) fourteenasphemorgue = E100#{&}#>#14
(403) fifteenasphemorgue = E100#{&}#>#15
(404) sixteenasphemorgue = E100#{&}#>#16
(405) seventeenasphemorgue = E100#{&}#>#17
(406) eighteenasphemorgue = E100#{&}#>#18
(407) nineteenasphemorgue = E100#{&}#>#19
(408) twentasphemorgue = E100#{&}#>#20
(409) thirtasphemorgue = E100#{&}#>#30
(410) fortasphemorgue = E100#{&}#>#40
(411) fiftasphemorgue = E100#{&}#>#50
(412) sixtasphemorgue = E100#{&}#>#60
(413) seventasphemorgue = E100#{&}#>#70
(414) eightasphemorgue = E100#{&}#>#80
(415) nintasphemorgue = E100#{&}#>#90
(416) hundrelasphemorgue = E100#{&}#>#100
(417) thousanasphemorgue = E100#{&}#>#1000
(418) myriadasphemorgue = E100#{&}#>#10,000
(419) millionasphemorgue = E100#{&}#>#1,000,000
(420) octadasphemorgue = E100#{&}#>#100,000,000
(421) sedeniadasphemorgue = E100#{&}#>#10,000,000,000,000,000
...
Rise out of the -asphemorgue series, moving on the old roots:
(422) blasphemorguliterator = E100#{&}#>#100
Which is also equal to:
(416) hundrelasphemorgue = E100#{&}#>#100
We can also have:
(423) grand blasphemorguliterator = E100#{&}#>#100#2
(424) grangol-carta-blasphemorguliterator = E100#{&}#>#100#100
(425) tethrathoth-carta-blasphemorguliterator = E100#{&}#>#100#^^#100
(426) blasphemorgulus-carta-blasphemorguliterator = E100#{&}#>#100#{&}#100
(427) tweilasphemorgue-carta-blasphemorguliterator = E100#{&}#>#100(#{&}#){&}#100
...
(428) blasphemorgulitertri = E100#{&}#>#100#{&}#>#100
(429) blasphemorgulitertet = E100#{&}#>#100#{&}#>#100#{&}#>#100
...
(430) blasphemorguliterator-by-hyperion = E100#{&}#>#*#100
(431) blasphemorguliterator-by-tethrathoth = E100#{&}#>#*#^^#100
(432) blasphemorguliterator-by-blasphemorgulus = E100#{&}#>#*#{&}#100
(433) blasphemorguliterator-by-tweilasphemorgue = E100#{&}#>#*(#{&}#){&}#100
...
(434) deutero-blasphemorguliterator = E100#{&}#>#*#{&}#>#100
(435) trito-blasphemorguliterator = E100#{&}#>#*#{&}#>#*#{&}#>#100
...
(436) blasphemorguliterfact = E100(#{&}#>#)^#100
(437) dutetrated-blasphemorguliterator = E100(#{&}#>#)^(#{&}#>#)100
...
(438) terrible blasphemorguliterator = E100(#{&}#>#)^^#100
(439) terrisquared blasphemorguliterator = E100(#{&}#>#)^^##100
(440) horrible blasphemorguliterator = E100(#{&}#>#)^^^#100
(441) horrendous blasphemorguliterator = E100(#{&}#>#)^^^^#100
(442) grievous blasphemorguliterator = E100(#{&}#>#){#}#100
(443) blasphemorgulnumus blasphemorguliterator = E100(#{&}#>#){#{&}#}#100
(444) tweilasphemorgulnumus blasphemorguliterator = E100(#{&}#>#){(#{&}#){&}#}#100
(445) blasphemorguliternumus blasphemorguliterator = E100(#{&}#>#){#{&}#>#}#100
(446) blasphemorgulitertaxitrisated-blasphemorguliterator = E100(#{&}#>#){(#{&}#>#){#{&}#>#}#}#100
...
(447) blasphemous blasphemorguliterator = E100(#{&}#>#){&}#100
(448) dis-blasphemous blasphemorguliterator = E100((#{&}#>#){&}#){&}#100
(449) tris-blasphemous blasphemorguliterator = E100(((#{&}#>#){&}#){&}#){&}#100
...
(450) blasphemorgulditerator = E100#{&}#>(#+#)100
(451) blasphemorgultriterator = E100#{&}#>(#+#+#)100
(451) blasphemorgulquadriterator = E100#{&}#>(#+#+#+#)100
Moving on:
(452) blasphemorgulgriditerator = E100#{&}#>##100
(also called (453) ludicriss)
(454) terrible blasphemorgulgriditerator = E100(#{&}#>##)^^#100
(455) blasphemorgulgriditernumus blasphemorgulgriditerator = E100(#{&}#>##){#{&}#>##}#100
(456) blasphemous blasphemorgulgriditerator = E100(#{&}#>##){&}#100
(457) blasphemorgulgriditer-iterator = E100#{&}#>(##+#)100
(458) blasphemorguldugriditerator = E100#{&}#>(##+##)100
(459) blasphemorgulcubiculator = E100#{&}#>###100
(460) blasphemorgulquarticulator = E100#{&}#>####100
...
(461) blasphemorgulspatialator = E100#{&}#>#^#100
(462) blasphemorgulgridispatialator = E100#{&}#>#^##100
(463) blasphemorgulsuperspatialator = E100#{&}#>#^#^#100
(464) blasphemorgulquadratetraditerator = E100#{&}#>#^#^#^#100
...
(465) tethrathoth-turreted-blasphemorgulus = E100#{&}#>#^^#100
(466) terrible-tethrathoth-turreted-blasphemorgulus = E100#{&}#>(#^^#)^^#100
(467) tethriterator-turreted-blasphemorgulus = E100#{&}#>#^^#>#100
(468) dustaculated-tethrathoth-turreted-blasphemorgulus = E100#{&}#>#^^#>#^^#100
(469) tethracross-turreted-blasphemorgulus = E100#{&}#>#^^##100
(470) tethracubor-turreted-blasphemorgulus = E100#{&}#>#^^###100
(471) tethrateron-turreted-blasphemorgulus = E100#{&}#>#^^####100
(472) tethratope-turreted-blasphemorgulus = E100#{&}#>#^^#^#100
(473) tethrarxitri-turreted-blasphemorgulus = E100#{&}#>#^^#^^#100
...
(474) pentacthulhum-turreted-blasphemorgulus = E100#{&}#>#^^^#100
(475) hexacthulhum-turreted-blasphemorgulus = E100#{&}#>#^^^^#100
(476) godsgodgulus-turreted-blasphemorgulus = E100#{&}#>#{#}#100
(477) godsgodgul-centurion-turreted-blasphemorgulus = E100#{&}#>#{#{#}#}#100
...
(478) dustaculated-blasphemorgulus = E100#{&}#>#{&}#100
(also called (479) blasphemorgudubbus)
(480) dustaculated-terrible-blasphemorgulus = E100#{&}#>(#{&}#)^^#100
(481) dustaculated-horrible-blasphemorgulus = E100#{&}#>(#{&}#)^^^#100
(482) dustaculated-grievous-blasphemorgulus = E100#{&}#>(#{&}#){#}#100
(483) dustaculated-blasphemorgulnumus-blasphemorgulus = E100#{&}#>(#{&}#){#{&}#}#100
(484) dustaculated-tweilasphemorgue = E100#{&}#>(#{&}#){&}#100
(485) dustaculated-blasphemorguliterator = E100#{&}#>#{&}#>#100
(486) dustaculated-tethrathoth-turreted-blasphemorgulus = E100#{&}#>#{&}#>#^^#100
(487) dustaculated-pentacthulhum-turreted-blasphemorgulus = E100#{&}#>#{&}#>#^^^#100
(488) dustaculated-godsgodgulus-turreted-blasphemorgulus = E100#{&}#>#{&}#>#{#}#100
...
(489) tristaculated-blasphemorgulus = E100#{&}#>#{&}#>#{&}#100
(also called (490) blasphemorgutrebbus)
(491) tristaculated-tweilasphemorgue = E100#{&}#>#{&}#>(#{&}#){&}#100
(492) tristaculated-blasphemorguliterator = E100#{&}#>#{&}#>#{&}#>#100
(493) tristaculated-tethrathoth-turreted-blasphemorgulus = E100#{&}#>#{&}#>#{&}#>#^^#100
(494) tristaculated-godsgodgulus-turreted-blasphemorgulus = E100#{&}#>#{&}#>#{&}#>{#}#100
(495) tetrastaculated-blasphemorgulus = E100#{&}#>#{&}#>#{&}#>#{&}#100
(also called (496) blasphemorguquabbus)
(497) pentastaculated-blasphemorgulus = E100#{&}#>#{&}#>#{&}#>#{&}#>#{&}#100 = E100#{&}##5
(498) hexastaculated-blasphemorgulus = E100#{&}#>#{&}#>#{&}#>#{&}#>#{&}#>#{&}#100 = E100#{&}##6
(499) hepastaculated-blasphemorgulus = E100#{&}#>#{&}#>#{&}#>#{&}#>#{&}#>#{&}#>#{&}#100 = E100#{&}##7
(500) octastaculated-blasphemorgulus = E100#{&}#>#{&}#>#{&}#>#{&}#>#{&}#>#{&}#>#{&}#>#{&}#100 = E100#{&}##8
(501) ennastaculated-blasphemorgulus = E100#{&}#>#{&}#>#{&}#>#{&}#>#{&}#>#{&}#>#{&}#>#{&}#>#{&}#100 = E100#{&}##9
(502) dekastaculated-blasphemorgulus = E100#{&}#>#{&}#>#{&}#>#{&}#>#{&}#>#{&}#>#{&}#>#{&}#>#{&}#>#{&}#100 = E100#{&}##10
...
(503) blasphemorgulcross = E100#{&}##100
(comparable to Saibian's agoraphobia)
How I stop at blasphemorgulcross? Let's refrain for the fundamental sequence of the two systems by Saibian's Hyper-Hyper-Extended Cascading-E notation (##xE^) after concluding the Hyper-Extended Cascading-E notation (#xE^) and my Collapsing-E notation (&E).
We know that:
{#,#,1,2}Â in ##xE^ = #{&}# in &E - The one equality
...
{{#,#,1,2},#,1,2} in ##xE^ ~ (#{&}#){&}# in &E
In ##xE^: FS of {{#,#,1,2},#,1,2} => {{#,#,1,2},#,1,2}[n+1] = {#,#,1,2}{({{#,#,1,2},#,1,2}[n])}{#,#,1,2}; {{#,#,1,2},#,1,2}[1] = {#,#,1,2}
In &E: FS of (#{&}#){&}# => (#{&}#){&}#[n+1] = (#{&}#){(#{&}#){&}#[n]}#; (#{&}#){&}#[1] = #{&}#
...
{{{#,#,1,2},#,1,2},#,1,2} in ##xE^ ~ ((#{&}#){&}#){&}# in &E
{{{{#,#,1,2},#,1,2},#,1,2},#,1,2} in ##xE^ ~ (((#{&}#){&}#){&}#){&}# in &E
{#,#+1,1,2} in ##xE^ ~ #{&}#># in &E
{{#,#+1,1,2},#,1,2} in ##xE^ ~ (#{&}#>#){&}# in &E
{{#,#+1,1,2},#+1,1,2} in ##xE^ ~ #{&}#>(#+#) in &E
...
&(1) in ##xE^ ~ #{&}#>## in &E
{&(1),#+1,1,2} in ##xE^ ~ #{&}#>(##+#) in &E
&(2) in ##xE^ ~ #{&}#>(##+##) in &E
&(3) in ##xE^ ~ #{&}#>(##+##+##) in &E
&(#) in ##xE^ ~ #{&}#>### in &E
&(##) in ##xE^ ~ #{&}#>#### in &E
&(#^#) in ##xE^ ~ #{&}#>#^# in &E
&(#^^#) in ##xE^ ~ #{&}#>#^^# in &E
&(#^^^#) in ##xE^ ~ #{&}#>#^^^# in &E
&(#^^^^#) in ##xE^ ~ #{&}#>#^^^^# in &E
&(#{#}#) in ##xE^ ~ #{&}#>#{#}# in &E
&(#{#{#}#}#) in ##xE^ ~ #{&}#>#{#{#}#}# in &E
&({#,#,1,2}) in ##xE^ ~ #{&}#>#{&}# in &E
&({#,#+1,1,2}) in ##xE^ ~ #{&}#>#{&}#># in &E
&(&(1)) in ##xE^ ~ #{&}#>#{&}#>## in &E
&(&({#,#,1,2})) in ##xE^ ~ #{&}#>#{&}#>#{&}# in &E
&(&(&(1))) in ##xE^ ~ #{&}#>#{&}#>#{&}#>## in &E
&(&(&({#,#,1,2}))) in ##xE^ ~ #{&}#>#{&}#>#{&}#>#{&}# in &E
&(&(&(&(1)))) in ##xE^ ~ #{&}#>#{&}#>#{&}#>#{&}#>## in &E
...
#*^# in ##xE^ ~ #{&}## in &E
{#*^#,#,1,2} in ##xE^ ~ (#{&}##){&}# in &E
{#*^#,#+1,1,2} in ##xE^ ~ (#{&}##){&}#># in &E
&(#*^#) in ##xE^ ~ (#{&}##){&}#>## in &E
&(&(#*^#)) in ##xE^ ~ (#{&}##){&}#>(#{&}##){&}#>## in &E
(#*^#)*^# in ##xE^ ~ (#{&}##){&}## in &E
((#*^#)*^#)*^# in ##xE^ ~ ((#{&}##){&}##){&}## in &E
#*^#># in ##xE^ ~ #{&}##># in &E
#*^#>{#,#,1,2} in ##xE^ ~ #{&}##>#{&}# in &E
#*^#>{#,#+1,1,2} in ##xE^ ~ #{&}##>#{&}#># in &E
#*^#>&(1) in ##xE^ ~ #{&}##>#{&}#>## in &E
#*^#>#*^# in ##xE^ ~ #{&}##>#{&}## in &E
#*^#>#*^#>#*^# in ##xE^ ~ #{&}##>#{&}##>#{&}## in &E
...
#*^## in ##xE^ ~ #{&}### in &E
#*^### in ##xE^ ~ #{&}#### in &E
#*^#### in ##xE^ ~ #{&}##### in &E
#*^#^# in ##xE^ ~ #{&}#^# in &E
#*^#^^# in ##xE^ ~ #{&}#^^# in &E
#*^#^^^# in ##xE^ ~ #{&}#^^^# in &E
#*^#{#}# in ##xE^ ~ #{&}#{#}# in &E
#*^{#,#,1,2} in ##xE^ ~ #{&}#{&}# in &E
#*^&(1) in ##xE^ ~ #{&}#{&}#>## in &E
#*^#*^# in ##xE^ ~ #{&}#{&}## in &E
#*^#*^#*^# in ##xE^ ~ #{&}#{&}#{&}## in &E
#*^#*^#*^#*^# in ##xE^ ~ #{&}#{&}#{&}#{&}## in &E
...
#*^^# in ##xE^ ~ #{&+1}# in &E
#*^^## in ##xE^ ~ #{&+1}## in &E
#*^^{#,#,1,2} in ##xE^ ~ #{&+1}#{&}# in &E
#*^^#*^# in ##xE^ ~ #{&+1}#{&}## in &E
#*^^#*^^# in ##xE^ ~ #{&+1}#{&+1}# in &E
#*^^#*^^#*^^# in ##xE^ ~ #{&+1}#{&+1}#{&+1}# in &E
#*^^^# in ##xE^ ~ #{&+2}# in &E
#*^^^^# in ##xE^ ~ #{&+3}# in &E
...
#*{#}# in ##xE^ ~ #{&+#}# in &E
#*{##}# in ##xE^ ~ #{&+##}# in &E
#*{#^#}# in ##xE^ ~ #{&+#^#}# in &E
#*{#^^#}# in ##xE^ ~ #{&+#^^#}# in &E
#*{#^^^#}# in ##xE^ ~ #{&+#^^^#}# in &E
#*{#{#}#}# in ##xE^ ~ #{&+#{#}#}# in &E
#*{#{#{#}#}#}# in ##xE^ ~ #{&+#{#{#}#}#}# in &E
#*{{#,#,1,2}}# in ##xE^ ~ #{&+#{&}#}# in &E
#*{&(1)}# in ##xE^ ~ #{&+#{&}#>##}# in &E
#*{#*^#}# in ##xE^ ~ #{&+#{&}##}# in &E
#*{#*^^#}# in ##xE^ ~ #{&+#{&+1}#}# in &E
#*{#*{#}#}# in ##xE^ ~ #{&+#{&+#}#}# in &E
#*{#*{{#,#,1,2}}#}# in ##xE^ ~ #{&+#{&+#{&}#}#}# in &E
#*{#*{#*^#}#}# in ##xE^ ~ #{&+#{&+#{&}##}#}# in &E
#*{#*{#*^^#}#}# in ##xE^ ~ #{&+#{&+#{&+1}#}#}# in &E
#*{#*{#*{#}#}#}# in ##xE^ ~ #{&+#{&+#{&+#}#}#}# in &E
#*{#*{#*{#*{#}#}#}#}# in ##xE^ ~ #{&+#{&+#{&+#{&+#}#}#}#}# in &E
...
*{#,#,1,2} in ##xE^ ~ #{&+&}# in &E
*{#,#+1,1,2} in ##xE^ ~ #{&+&}#># in &E
*&(1) in ##xE^ ~ #{&+&}#>## in &E
*&(#) in ##xE^ ~ #{&+&}#>### in &E
*&(*&(#)) in ##xE^ ~ #{&+&}#>#{&+&}#>### in &E
*&(*&(*&(#))) in ##xE^ ~ #{&+&}#>#{&+&}#>#{&+&}#>### in &E
#**^# in ##xE^ ~ #{&+&}## in &E
#**^^# in ##xE^ ~ #{&+&+1}# in &E
#**^^^# in ##xE^ ~ #{&+&+2}# in &E
#**{#}# in ##xE^ ~ #{&+&+#}# in &E
...
**{#,#,1,2} in ##xE^ ~ #{&+&+&}# in &E
**&(#) in ##xE^ ~ #{&+&+&}#>### in &E
**&(**&(#)) in ##xE^ ~ #{&+&+&}#>#{&+&+&}#>### in &E
#***^# in ##xE^ ~ #{&+&+&}## in &E
#***^^# in ##xE^ ~ #{&+&+&+1}# in &E
#***^^^# in ##xE^ ~ #{&+&+&+2}# in &E
***{#,#,1,2} in ##xE^ ~ #{&+&+&+&}# in &E
***&(#) in ##xE^ ~ #{&+&+&+&}#>### in &E
***&(***&(#)) in ##xE^ ~ #{&+&+&+&}#>#{&+&+&+&}#>### in &E
#****^# in ##xE^ ~ #{&+&+&+&}## in &E
#*****^# in ##xE^ ~ #{&+&+&+&+&}## in &E
#******^# in ##xE^ ~ #{&+&+&+&+&+&}## in &E
...
*(#) in ##xE^ ~ #{&#}# in &E
*(#+1) in ##xE^ ~ #{&#+&}# in &E
*(#+#) in ##xE^ ~ #{&#+&#}# in &E
*(##) in ##xE^ ~ #{&##}# in &E
*(###) in ##xE^ ~ #{&###}# in &E
*(#^#) in ##xE^ ~ #{&#^#}# in &E
*(#^^#) in ##xE^ ~ #{&#^^#}# in &E
*(#^^^#) in ##xE^ ~ #{&#^^^#}# in &E
*(#{#}#) in ##xE^ ~ #{&#{#}#}# in &E
*({#,#,1,2}) in ##xE^ ~ #{&#{&}#}# in &E
*({#,#+1,1,2}) in ##xE^ ~ #{&#{&}#>#}# in &E
*(&(1)) in ##xE^ ~ #{&#{&}#>##}# in &E
*(#*^#) in ##xE^ ~ #{&#{&}##}# in &E
*(#*^^#) in ##xE^ ~ #{&#{&+1}#}# in &E
*(#*{#}#) in ##xE^ ~ #{&#{&+#}#}# in &E
*(*{#,#,1,2}) in ##xE^ ~ #{&#{&+&}#}# in &E
*(**{#,#,1,2}) in ##xE^ ~ #{&#{&+&+&}#}# in &E
...
*(*(#)) in ##xE^ ~ #{&#{&#}#}# in &E
*(*(*(#))) in ##xE^ ~ #{&#{&#{&#}#}#}# in &E
*(*(*(*(#)))) in ##xE^ ~ #{&#{&#{&#{&#}#}#}#}# in &E
etc.
And finally...
#/^# in Solidus-Extended Cascading-E Notation (/xE^) ~ #{&&}# in &E
After the limit of the Saibian's Hyper-Hyper-Extended Cascading-E notation, I have some decent comparison between Saibian's Solidus-Extended Cascading-E notation.
Here are some examples:
(#/^#)^^# in /xE^ ~ (#{&&}#)^^# in &E
(#/^#)^^^# in /xE^ ~ (#{&&}#)^^^# in &E
(#/^#){#}# or {#/^#,#,#} in /xE^ ~ (#{&&}#){#}# in &E
Pause for a while and let's refine the sequence because it looks awkward and ugly...
{#/^#,#,{#/^#,#,#}} in /xE^ ~ (#{&&}#){#{&&}#}# in &E
{#/^#,#,{#/^#,#,{#/^#,#,#}}} in /xE^ ~ (#{&&}#){(#{&&}#){#{&&}#}#}# in &E
...
{#/^#,#,1,2} in /xE^ ~ (#{&&}#){&}# in &E
{#/^#,#+1,1,2} in /xE^ ~ (#{&&}#){&}#># in &E
&(#/^#+1) in /xE^ ~ (#{&&}#){&}#>## in &E
...
(#/^#)*^# in /xE^ ~ (#{&&}#){&}## in &E
(#/^#)*^## in /xE^ ~ (#{&&}#){&}### in &E
(#/^#)*^#^# in /xE^ ~ (#{&&}#){&}#^# in &E
(#/^#)*^#^^# in /xE^ ~ (#{&&}#){&}#^^# in &E
(#/^#)*^{#,#,1,2} in /xE^ ~ (#{&&}#){&}#{&}# in &E
(#/^#)*^(#/^#) in /xE^ ~ (#{&&}#){&}(#{&&}#) in &E
...
(#/^#)*^^# in /xE^ ~ (#{&&}#){&+1}# in &E
(#/^#)*^^^# in /xE^ ~ (#{&&}#){&+2}# in &E
...
*{#/^#,#,#} in /xE^ ~ (#{&&}#){&+#}# in &E
*{#/^#,#,#/^#} in /xE^ ~ (#{&&}#){&+#{&&}#}# in &E
*{#/^#,#,*{#/^#,#,#}} in /xE^ ~ (#{&&}#){&+(#{&&}#){&+#}#}# in &E
...
*{#/^#,#,1,2} in /xE^ ~ (#{&&}#){&+&}# in &E
*{#/^#,#+1,1,2} in /xE^ ~ (#{&&}#){&+&}#># in &E
*&(#/^#+1) in /xE^ ~ (#{&&}#){&+&}#>## in &E
(#/^#)**^# in /xE^ ~ (#{&&}#){&+&}## in &E
(#/^#)**^^# in /xE^ ~ (#{&&}#){&+&+1}# in &E
...
(#/^#)***^# in /xE^ ~ (#{&&}#){&+&+&}# in &E
(#/^#)****^# in /xE^ ~ (#{&&}#){&+&+&+&}# in &E
(#/^#)*****^# in /xE^ ~ (#{&&}#){&+&+&+&+&}# in &E
...
(#/^#)*{#}^# in /xE^ ~ (#{&&}#){&#}# in &E
(#/^#)*{#/^#}^# in /xE^ ~ (#{&&}#){&#{&&}#}# in &E
(#/^#)*{(#/^#)*{#}^#}^# in /xE^ ~ (#{&&}#){&(#{&&}#){&#}#}# in &E
This will not converge with the comparisons above...
*(#){#/^#,#,1,2} in /xE^ ~ (#{&&}#){&#{&}#}# in &E
*(*(#)){#/^#,#,1,2} in /xE^ ~ (#{&&}#){&#{&+&}#}# in &E
*(*(*(#))){#/^#,#,1,2} in /xE^ ~ (#{&&}#){&#{&+&+&}#}# in &E
And the expression becomes uglier...
*(#/^#) or *(#/^#){#/^#,#,1,2} in /xE^ ~ (#{&&}#){&&}# in &E
*(*(#/^#)) in /xE^ ~ ((#{&&}#){&&}#){&(#{&&}#){&&}#}# in &E
*(*(*(#/^#))) in /xE^ ~ ((#{&&}#){&&}#){&((#{&&}#){&&}#){&(#{&&}#){&&}#}#}# in &E
...
*** This makes Saibian's solidi STOP!!! ***
(#/^#)/^# in /xE^ ~ ((#{&&}#){&&}#){&&}# in &E
((#/^#)/^#)/^# in /xE^ ~ (((#{&&}#){&&}#){&&}#){&&}# in &E
(((#/^#)/^#)/^#) in /xE^ ~ ((((#{&&}#){&&}#){&&}#){&&}#){&&}# in &E
...
#/^#># in /xE^ ~ #{&&}#># in &E
#/^#>#/^# in /xE^ ~ #{&&}#>#{&&}# in &E
...
#/^## in /xE^ ~ #{&&}## in &E
#/^### in /xE^ ~ #{&&}### in &E
#/^#### in /xE^ ~ #{&&}#### in &E
#/^#^# in /xE^ ~ #{&&}#^# in &E
#/^#^^# in /xE^ ~ #{&&}#^^# in &E
#/^{#,#,1,2} in /xE^ ~ #{&&}#{&}# in &E
...
#/^#/^# in /xE^ ~ #{&&}#{&&}# in &E
#/^#/^#/^# in /xE^ ~ #{&&}#{&&}#{&&}# in &E
...
#/^^# in /xE^ ~ #{&&+1}# in &E
#/^^^# in /xE^ ~ #{&&+2}# in &E
#/^^^^# in /xE^ ~ #{&&+3}# in &E
...
#/{#}# or /{#,#,#} in /xE^ ~ #{&&+#}# in &E
#/{#}# or /{#,#,/{#,#,#}} in /xE^ ~ #{&&+#{&&+#}#}# in &E
...
/{#,#,1,2} in /xE^ ~ #{&&+&}# in &E
/{#,#+1,1,2} in /xE^ ~ #{&&+&}#># in &E
/&(1) in /xE^ ~ #{&&+&}#>## in &E
/#*^# in /xE^ ~ #{&&+&}## in &E
/#*^^# in /xE^ ~ #{&&+&+1}# in &E
/#*^^^# in /xE^ ~ #{&&+&+2}# in &E
/#*{#}# in /xE^ ~ #{&&+&+#}# in &E
...
#/*^# in /xE^ ~ #{&&+&+&}# in &E
#/**^# in /xE^ ~ #{&&+&+&+&}# in &E
#/***^# in /xE^ ~ #{&&+&+&+&+&}# in &E
...
/*(#){#,#,1,2} in /xE^ ~ #{&&+&#}# in &E
/*(/*(#){#,#,1,2}){#,#,1,2} in /xE^ ~ #{&&+&#{&&+&#}#}# in &E
...
#//^# in /xE^ ~ #{&&+&&}# in &E
#//^^# in /xE^ ~ #{&&+&&+1}# in &E
//{#,#,#} in /xE^ ~ #{&&+&&+#}# in &E
#//*^# in /xE^ ~ #{&&+&&+&}# in &E
//*(#){#,#,1,2} in /xE^ ~ #{&&+&&+&#}# in &E
...
#///^# in /xE^ ~ #{&&+&&+&&}# in &E
#////^# in /xE^ ~ #{&&+&&+&&+&&}# in &E
#/////^# in /xE^ ~ #{&&+&&+&&+&&+&&}# in &E
...
#/(#)^# in /xE^ ~ #{&&#}# in &E
#/({#,#,1,2})^# in /xE^ ~ #{&&#{&}#}# in &E
...
#/(#/^#)^# in /xE^ ~ #{&&#{&&}#}# in &E
#/(#//^#)^# in /xE^ ~ #{&&#{&&+&&}#}# in &E
#/(#///^#)^# in /xE^ ~ #{&&#{&&+&&+&&}#}# in &E
#/(#/(#)^#)^# in /xE^ ~ #{&&#{&&#}#}# in &E
...
#/(#/(#/^#)^#)^# in /xE^ ~ #{&&#{&&#{&&}#}#}# in &E
#/(#/(#/(#/^#)^#)^#)^# in /xE^ ~ #{&&#{&&#{&&#{&&}#}#}#}# in &E
#/(#/(#/(#/(#/^#)^#)^#)^#)^# in /xE^ ~ #{&&#{&&#{&&#{&&#{&&}#}#}#}#}# in &E
...
#/x^# in /xE^ ~ #{&&&}# in &E
#/x^^# in /xE^ ~ #{&&&+1}# in &E
#/x{#,#,#} in /xE^ ~ #{&&&+#}# in &E
#/x*^# in /xE^ ~ #{&&&+&}# in &E
#/x/^# in /xE^ ~ #{&&&+&&}# in &E
/x/(#) in /xE^ ~ #{&&&+&&#}# in &E
...
#/x/x^# in /xE^ ~ #{&&&+&&&}# in &E
#/x/x/x^# in /xE^ ~ #{&&&+&&&+&&&}# in &E
#/x/x/x/x^# in /xE^ ~ #{&&&+&&&+&&&+&&&}# in &E
...
/x(#){#,#,1,2} in /xE^ ~ #{&&&#}# in &E
/x(/x(#)) in /xE^ ~ #{&&&#{&&&#}#}# in &E
/x(/x(/x(#))) in /xE^ ~ #{&&&#{&&&#{&&&}#}#}# in &E
...
#/xx^# in /xE^ ~ #{&&&&}# in &E
#/xx/xx^# in /xE^ ~ #{&&&&+&&&&}# in &E
/xx(#) in /xE^ ~ #{&&&&#}# in &E
/xx(/xx(#)) in /xE^ ~ #{&&&&#{&&&&#}#}# in &E
...
#/xxx^# in /xE^ ~ #{&&&&&}# in &E
#/xxxx^# in /xE^ ~ #{&&&&&&}# in &E
#/xxxxx^# in /xE^ ~ #{&&&&&&&}# in &E
#/xxxxxx^# in /xE^ ~ #{&&&&&&&&}# in &E
...
And this reaches the small Veblen ordinal...
#(x^#)^# or x^# in /xE^ ~ #{&^#}# in &E
x^#*x in /xE^ ~ #{&^#*&}# in &E
x^#*x^# in /xE^ ~ #{&^#*&^#}# in &E
x^## in /xE^ ~ #{&^##}# in &E
x^### in /xE^ ~ #{&^###}# in &E
x^#^# in /xE^ ~ #{&^#^#}# in &E
x^#^^# in /xE^ ~ #{&^#^^#}# in &E
x^{#,#,1,2} in /xE^ ~ #{&^#{&}#}# in &E
x^(#/^#) in /xE^ ~ #{&^#{&&}#}# in &E
x^(#/x^#) in /xE^ ~ #{&^#{&&&}#}# in &E
x^(#/xx^#) in /xE^ ~ #{&^#{&&&&}#}# in &E
x^(#/xxx^#) in /xE^ ~ #{&^#{&&&&&}#}# in &E
...
x^x^# in /xE^ ~ #{&^#{&^#}#}# in &E
x^x^x^# in /xE^ ~ #{&^#{&^#{&^#}#}#}# in &E
x^x^x^x^# in /xE^ ~ #{&^#{&^#{&^#{&^#}#}#}#}# in &E
x^x^x^x^x^# in /xE^ ~ #{&^#{&^#{&^#{&^#{&^#}#}#}#}#}# in &E
...
And the limit reaches the large Veblen ordinal...
x^^# in /xE^ ~ #{&^&}# in &E
There is an ad hoc ExE size comparison:
x^^#*x in /xE^ ~ #{&^&*&}# in &E
x^^#*x^^# in /xE^ ~ #{&^&*&^&}# in &E
(x^^#)^# in /xE^ ~ #{&^&#}# in &E
(x^^#)^#^# in /xE^ ~ #{&^&#^#}# in &E
(x^^#)^#^^# in /xE^ ~ #{&^&#^^#}# in &E
(x^^#)^{#,#,1,2} in /xE^ ~ #{&^&#{&}#}# in &E
(x^^#)^#/^# in /xE^ ~ #{&^&#{&&}#}# in &E
(x^^#)^#/x^# in /xE^ ~ #{&^&#{&&&}#}# in &E
(x^^#)^(x^#) in /xE^ ~ #{&^&#{&^#}#}# in &E
(x^^#)^(x^x^#) in /xE^ ~ #{&^&#{&^#{&}#}#}# in &E
(x^^#)^(x^^#) in /xE^ ~ #{&^&#{&^&}#}# in &E
(x^^#)^(x^^#)^(x^^#) in /xE^ ~ #{&^&#{&^&#{&^&}#}#}# in &E
(x^^#)^^# in /xE^ ~ #{&^&&}# in &E
(x^^#)^^(x^^#) in /xE^ ~ #{&^&&#{&^&&}#}# in &E
(x^^#)^^^# in /xE^ ~ #{&^&&&}# in &E
(x^^#)^^^^# in /xE^ ~ #{&^&&&&}# in &E
(x^^#){#}# in /xE^ ~ #{&^&^#}# in &E
...
But, it will get so awkward after this point, so that /_2 would be comparable to the limit of the Collapsing-E notation, which is the Bachmann-Howard ordinal.
With the last two numbers using the Solidus-Extended Cascading-E Notation:
babbulbufihgh ~ E100#{&_2}#100 in x&E (the limit of &E as it is equal to E100#{&^&^&^&^ ... ... ^&^&^&^&}#100 w/ 100 &'s)
solidifihgh ~ E100#{&_&_&_&_&_ ... ... ... _&_&_&_&_&}#100 w/ 100 &'s in #x&E (the limit, intended, as the definition is not yet proposed)
*** MIGAWD ***
After the discussion regarding the Solidus-Extended Cascading-E notation in comparison, let's return to the &E and continue beyond blasphemorgulcross!
(102) blasphemorgulcubor = E100#{&}###100
(comparable to astralthrathoth)
(103) blasphemorgulteron = E100#{&}####100
...
(104) blasphemorgultope = E100#{&}#^#100
(105) blasphemorgularxitri = E100#{&}#{&}#100
(106) blasphemorgularxitet = E100#{&}#{&}#{&}#100
Then...
(107) blasphemorgulhenus = E100#{&+1}#100
(also called (108) greesblasphemorgulus)
(109) blasphemous blasphemorgulhenus = E100(#{&+1}#){&}#100
(110) blasphemorgulhenaldubbus = E100(#{&+1}#){&+1}#100
(111) blasphemorgulhenaliterator = E100#{&+1}#>#100
(112) dustaculated-blasphemorgulhenus = E100#{&+1}#>#{&+1}#100
(113) blasphemorgulhenuecross = E100#{&+1}##100
(114) blasphemorgulhenuetope = E100#{&+1}#^#100
(115) blasphemorgulhenuarxitri = E100#{&+1}#{&+1}#100
...
(116) blasphemorguldeuterus = E100#{&+2}#100
(117) blasphemorgultritus = E100#{&+3}#100
(118) blasphemorgultetertus = E100#{&+4}#100
...
(119) blasphemorgulhyperius = E100#{&+#}#100
(120) blasphemorguldihyperius = E100#{&+#+#}#100
(121) blasphemorgulgridihyperius = E100#{&+##}#100
(122) blasphemorgulgodgahlahius = E100#{&+#^#}#100
(123) blasphemorgultethrathothius = E100#{&+#^^#}#100
...
(124) blasphemorgulversiadyon = E100#{&+#{&}#}#100
(125) blasphemorgulversed-blasphemorgulhenus = E100#{&+#{&+1}#}#100
...
(126) blasphemorgulversiatrion = E100#{&+#{&+#{&}#}#}#100
And making more fundamental sequences...
(127) blasphemordeus = E100#{&+&}#100
= E100#{&+#{&+#{...&+#{&+#{&}#}#...}#}#}#100
w/ 100 &'s
(128) blasphemortruce = E100#{&+&+&}#100
(129) blasphemorquad = E100#{&+&+&+&}#100
...
(130) blasphemorhyperiath = E100#{&#}#100
(131) blasphemoriasi-tethrathoth = E100#{&#^^#}#100
...
(132) blasphemoriadeusus = E100#{&#{&}#}#100
(133) blasphemoriatreusus = E100#{&#{&#{&}#}#}#100
...
(134) squariduagulus = E100#{&&}#100
= E100#{&#{&#{...&#{&#{&}#}#}#}#}#100
w/ 100 &'s
(135) squariduaguldeus = E100#{&&+&&}#100
(136) squariduagulhyperiath = E100#{&&#}#100
(137) squariduadiadeusus = E100#{&&#{&&}#}#100
...
(138) cubiculgulus = E100#{&&&}#100
(139) quarticulgulus = E100#{&&&&}#100
...
(140) hypericulgulus = E100#{&^#}#100
(141) hypericulastraduas = E100#{&^#{&}#}#100
(142) hypericulastratrias = E100#{&^#{&^#{&}#}#}#100
...
(143) spatialatigulus = E100#{&^&}#100
= E100#{&^#{&^#{...&^#{&^#{&}#}#...}#}#}#100
w/ 100 &'s
(144) dyalspatialatigulus = E100#{&^&&}#100
(145) tryalspatialatigulus = E100#{&^&&&}#100
...
(146) hyperialspatialatigulus = E100#{&^&^#}#100
(147) spatialatici-astraduas = E100#{&^&^#{&^&}#}#100
...
(148) spatialtritigulus = E100#{&^&^&}#100
(149) spatialtetertigulus = E100#{&^&^&^&}#100
(150) spatialpeptigulus = E100#{&^&^&^&^&}#100
(151) spatialextigulus = E100#{&^&^&^&^&^&}#100
...
(152) spatialdekatigulus = E100#{&^&^&^&^&^&^&^&^&^&}#100
And finally,
(153) blasteriagulus = E100#{&^^#}#100
(also called (154) spatialhecatigulus)
= E100#{&^&^&^&^...^&^&^&^&}#100
w/ 100 &'s
To be continued...