Now we passed the major milestone of the Collapsing-E notation!
(1210) squariduagulus = E100#{&&}#100 [φ(1, 0, 0, 0, 0) | ψ(Ω^Ω^3) | #/^#]
= E100#{&#{&#{...&#{&#{&}#}#}#}#}#100
w/ 100 &'s
(also called (1211) blasphemoriacenteuon. Comparable to Saibian's "transmorgrifihgh", defined using his ad hoc extension known as "Solidus-Extended Cascading-E notation", which is the successor of "Hyper-Hyper-Extended Cascading-E notation")
Before we continue further, we have to recap somehow about the Solidus-Extended Cascading-E notation Saibian created that would be very awkward.
(135) squariduaguldeus = E100#{&&+&&}#100 [φ(2, 0, 0, 0, 0) | ψ(Ω^(Ω^3·2))]
(136) squariduagulhyperiath = E100#{&&#}#100 [φ(ω, 0, 0, 0, 0) | ψ(Ω^(Ω^3·ω))]
(137) squariduadiadeusus = E100#{&&#{&&}#}#100 [φ(φ(1, 0, 0, 0, 0), 0, 0, 0, 0) | ψ(Ω^(Ω^3·ψ(Ω^(Ω^3))))]
...
(138) cubiculgulus = E100#{&&&}#100 [φ(1, 0, 0, 0, 0, 0) | ψ(Ω^Ω^4)]
(139) quarticulgulus = E100#{&&&&}#100 [φ(1, 0, 0, 0, 0, 0, 0) | ψ(Ω^Ω^5)]
...
And now we passed the small Veblen ordinal...
(140) hypericulgulus = E100#{&^#}#100 [φ(1 @{ω}) | ψ(Ω^Ω^ω)]
(141) hypericulastraduas = E100#{&^#{&}#}#100 [φ(1 @{φ(1, 0, 0, 0)}) | ψ(Ω^Ω^ψ(Ω^Ω^2))]
(142) hypericulastratrias = E100#{&^#{&^#{&}#}#}#100 [φ(1 @{φ(1 @{φ(1, 0, 0, 0)})}) | ψ(Ω^Ω^ψ(Ω^Ω^ψ(Ω^Ω^2)))]
...
And then the large Veblen ordinal!
(143) spatialatigulus = E100#{&^&}#100 [φ(1 @{1, 0}) | ψ(Ω^Ω^Ω)]
= E100#{&^#{&^#{...&^#{&^#{&}#}#...}#}#}#100
w/ 100 &'s
(144) dyalspatialatigulus = E100#{&^&&}#100 [φ(1 @{1, 0, 0}) | ψ(Ω^Ω^Ω^2)]
(145) tryalspatialatigulus = E100#{&^&&&}#100 [φ(1 @{1, 0, 0, 0}) | ψ(Ω^Ω^Ω^3)]
...
(146) hyperialspatialatigulus = E100#{&^&^#}#100 [φ(1 @{1 @{ω}}) | ψ(Ω^Ω^Ω^ω)]
(147) spatialatici-astraduas = E100#{&^&^#{&^&}#}#100 [φ(1 @{1 @{φ(1 @{1, 0})}}) | ψ(Ω^Ω^Ω^ψ(Ω^Ω^Ω))]
...
(148) spatialtritigulus = E100#{&^&^&}#100 [φ(1 @{1 @{1, 0}}) | ψ(Ω^Ω^Ω^Ω)]
(149) spatialtetertigulus = E100#{&^&^&^&}#100 [φ(1 @{1 @{1 @{1, 0}}}) | ψ(Ω^Ω^Ω^Ω^Ω)]
(150) spatialpeptigulus = E100#{&^&^&^&^&}#100 [φ(1 @{1 @{1 @{1 @{1, 0}}}}) | ψ(Ω^Ω^Ω^Ω^Ω^Ω)]
(151) spatialextigulus = E100#{&^&^&^&^&^&}#100 [φ(1 @{1 @{1 @{1 @{1 @{1, 0}}}}}) | ψ(Ω^Ω^Ω^Ω^Ω^Ω^Ω)]
...
(152) spatialdekatigulus = E100#{&^&^&^&^&^&^&^&^&^&}#100
[φ(1 @{1 @{1 @{1 @{1 @{1 @{1 @{1 @{1 @{1, 0}}}}}}}}}) | ψ(Ω^Ω^Ω^Ω^Ω^Ω^Ω^Ω^Ω^Ω^Ω)]
And finally,
(153) blasteriagulus = E100#{&^^#}#100 [BHO]
(also called (154) spatialhecatigulus)
= E100#{&^&^&^&^...^&^&^&^&}#100
w/ 100 &'s
Next sneak peek - 9 (COMING SOON!)