☐ⱴ - TNAN [Definition] ░ⱴ < ▒ⱴ < ▓ⱴ < █ⱴ A Powerset Cascade is where you nest Powerset n-levels upon themselves n-times, and repeat this n times to the point of being unable to go back down to a singular powerset. Powerset levels are collections of nested Powersets that are nested n times. PCℵCC(ℵCC) = ░ⱴ PC░ⱴCC(░ⱴCC) = ▒ⱴ PC▒ⱴCC(▒ⱴCC) = ▓ⱴ PC▓ⱴCC(▓ⱴCC) = █ⱴ PC█ⱴ(█ⱴ) = █ⱴ_1 This cycles, resulting in █ⱴCC, which is a higher order of ⟳, being equivalent to PC⟳C(⟳C), or a cascade of ⟳ within a powerset cascade of ⟳C. When you apply ☐ⱴ to any number, use this chart for it. ░ⱴ([1,2,3,...,ω-1]), you get ω, for ░ⱴ(ℵ0) you get ℵC, for ░ⱴ(░ⱴ) you get ░ⱴ. █ⱴCC(█ⱴCC) and PC█ⱴCC(█ⱴCC) = █ⱴCC, which is the upper bound. any ☐ⱴ +1 is equivalent to -☐ⱴ.
stuff ☐ɕ is equivalent to ω within a sense of it.
