We are starting from Aleph null.-The first smallest infinity! Then we hit Aleph_Omega. Wich is a bigger infinity then the other alephs below it. Then whats beyond them? Aleph null----------Aleph omega-------θ We hit something here. Its an ineccible cardinal called transinfinity the smallest transinfinity.
We hit then a other thing called Theta_one. Or the second smallest transinfinity θ+1 And then comes θ+2 θ+3 θ+4 and so one........
As we see on the picture. This is an inecceible smallest transinfinity after we hit those Theta pluses we hit a bigger transinfinity called. θ1 Or theta 1. θ2 θ3 θ4 θ5... All the way out to θ_omega! So we can reach θxθ or we can do a bigger trasinfinity cardinal Then θ×θ + 1, θ×θ + 2, ... θxθ + ω, ... θ×(θ + 1), ... θ×(θ×θ), θ^3 ... θ^ω, ... θ^θ............. Then we reached ℵ_(θ+1) ℵ_(θ+2)....... ℵ_(θ+w)..... ℵ_(θ+w+1) Or we might reach. ℵ(θ+ξ3) ℵ(θ+θ) ℵ(θ+θ+1) ℵ_(θxθ+2).... Then we reached after that
Now when we continue ℵ(θ+θ+θ+θ+θ+θ),,,,,.......... Then now we reached. ℵ(θ^θ^θ^θ^θE+θxθxθ+θ+θ+θ+ℵ+ℵ+ℵE+1100) Thats a larger transinfinity then the other one above this ^^^^^^^^^...... So theres clearly nothing beyond them? Right? Eehh well there might be a other cardinal. So big so large so N huge. That no powersetting a transinfinity number making omega amounts of anything. Or even a POWERSETTING A larger transinfinity... To get you nothing. But a other transinfinity. Sure a ℵ(θ+θ+θ+θ+θ+θxθxθE+θ+θE+3438 Is really big. But its still just a transinfinity!! Not even close to the that number. The larger then ever transinfinites. If I am correct. There might be a other cardinal thats inecceible thats larger then all transinfinties. But! What if something called.. -Omegainfinity.. Omegainfinity is a ineccecible cardinal that is so big then ever. It would take forever! To get there. Not if we create a other axiom! So we can name the Omegainfinity to ט This cardinal cannot be reached...
It would take forever ט........ But there might be ט1 ט
But thats to far Omegainfinite But we can still reach it! We now entered ט the first smallest Omegainfinity.... ט sounds stupid but all of the transinfinity cardinals was well ordered so we reached ט now we continue to 1ט2 ט. ...... Now we are reaching More then that... But thats uncountble... So Omegainfinity looks like that.
ט,,,,,,,,,,,,,,,,......................______Now we reached a even bigger then every Omegainfinity ever.
ℵ(ט+1)....ℵ(ט+2),,,,,.....____ I continue later. As for now. Thanks for reading this.