User blog comment:TySkyo/Maxigoogol/@comment-24920136-20160803212455/@comment-28633611-20160804164224

How do you put LATEX in your comments?

I tried various methods and all of them failed.

At any rate, x is definitely not bigger than J^450 of anything. When you have a number such as this, the two most important things (in that order) are:

1. The number of iterations of the knuth arrows in the definition of x (which seems to be 99)

2. The number of arrows in the top row of the definition of x (which is 10^10^...^10^100 with 100 tens)

Everything else, including all the other power towers, has a completely negligible effect on the size of the final number. You could replace all those power towers with "10's" and you'll get pretty much the same result. So:

x ~ J^99(E^99(100)) ~ J^99(10^^100)

Now, x is so large, that doing (10^^100)^x doesn't change it by much, so we can write the Ackerman function as:

Maxigoogol ~ A(x,x)

The second 'x' is - again - completely irelevant. A(x,x) is virtually indistinguishable from A(x,10) which - in turn - is indisinguishable from Jx.

So:

Maxigoogol ~ Jx ~ J(J^99(10^^100)) = J^100(10^^100).

Which is between the 100th and 101st iteration of Graham's number:

G_100 ~ J^100(4) < J^100(10^^100) < J^100(10^^^10) = J^101(3) < G_101