So, you made it through the first list without crying. Well done, and welcome to this MUCH larger list. Omega was just a primer. Have fun! =)
We've already shown these entries, but this is just a recap of our current position. Onward!
This is also 2 in a Mega-gon using Steinhaus-Moser notation. The above notation is Hyper-Moser notation. A Mega-gon is not to be confused with a megagon, which has 1 million sides. This is a polygon with Mega sides, where mega is 2 in a pentagon, which is a HUGE difference.
Big number. Yay.
This is not to be confused with Graham's number, which is MUCH larger. Here, F(x) is equal to {2,3,x}, so this number is also equivalent to {2,3,{2,3,{2,3,{2,3,{2,3,{2,3,{2,3,12}}}}}}}.
Another FGH milestone from Denis Maksudov, we've reached omega plus one now! This is the growth rate of expansion, so soon we'll surpass Graham's number.
Speaking of which, here it is! This is probably the most famous large number, and it's quite big, but NOT BIG ENOUGH.
And here's our next hyper-operator/BEAF googolism. This is 10 expanded to 100. Since this is a BEAF googolism, next up has to be...
...a Saibianism! It's a simple pattern. Most major BEAF numbers have a major ExE number to go with them. In this case, Ea##a#b is roughly {a,b,1,2} in BEAF.
Here's another Graham Function number. This one was coined by Aarex.
Thanks Denis, more FGH numbers for the list! We've reached a new FGH level, meaning there must be a new hyper-operator. And sure enough...
...there is! Coined by Cookie Fonster, alternate name of Kil-Doogol from Username. Now remember the pattern...
And sure enough, it works! Do note that the converse does not work, many major Saibianisms do not have BEAF counterparts. (but this is common only much later)
Another "Fonsterism", and also another "Usernamism", as Username calls this Kil-Toogol.
I'll skip past some numbers to reach our next major number.
For once, the BEAF number comes AFTER the Saibianism. Whatever, let's go to our next number!
This is also 10 centiexpanded to 10. Now next, we have an FGH number.
This is quite a large number in the FGH. However, we're only at the omega level of the FGH, and we can go MUCH further.
This is at the growth rate of explosion, so next up is another new number in BEAF.
This is 10 exploded to 100 = 10{{10{{10{{10...10{{10}}10...10}}10}}10}}10 w/ 100 10's on either side, center included.
And another Saibianism.