Is it larger than 10!!!!!!!!!? (each being a factorial)

Ricky, your number is peanuts.
Think of 3^3^3^3^3
This number is just about the start of Graham's number which extends to 63 layers.
Please use a search engine and search for Graham's number.
Factorials are nothing compared to iterations.
I shall try to explain in a simple way.
3+3 is the first stage.
The next is 3x3.
The next is 3^3.
What next?
The stage is called tetration. (I think)
3^^3.
and then would come
3^^^3.
The number you have given is less than the first level of Graham's Number.

Ricky wrote:

Is it larger than 10!!!!!!!!!? (each being a factorial)

I thought that adding extra factorials made the result smaller because some of the multipliers are skipped.

For example, 5!! is 5*3*1 = 15.
So 10!!!!!!!!! would be 10*2, which is 20.

Ganesh, 10!!, as you said, is 3628800!.  That's 3628800*3628799*3628798*368797....

That's only the first four terms, and it's already 173,400,926,419,517,324,430,067,200

The first 4 terms of a 3,628,800 factorial is already 27 digits long, and that's only the 2nd factorial of 9.  Imagine just taking the factorial of the number above.

I tried to get mathimatica to do (10!)! but it keeps on crashing.  Anyone else have any luck?

Ricky,
I am sorry I was wrong in post # 9.
I didn't use Arithmetica or any computer,
just James Stirling formula which gives very close approximation for higher values of factorials.
The formula is n!=sqrt2*pi*n (n/e)^n
Therefore if the number of factorials is 10, your number may be greater.
However, I am sure it is lesser than 10^10^10^....20 times ^10.

By the way, in response to your question,"What an interesting comparison - which one packs the most punch?" concerning factorials and up-arrow notation, I'm pretty sure that up-arrow notation is the whopper, though I can't say for sure.

Oh, definitely. Even just a googol is more than the amount of electrons in the universe, and a googol is absolutely titchy compared with some of the other numbers mentioned in this thread.

I would also agree that Up Arrow notation makes bigger numbers than factorials, but I'm also not entirely sure.

Welcome to the forum, by the way. Very interesting name you have there.

Yeah , it's pretty big , 

Let me see if I can explain the first steps of the number here:

1 Take the first step : 3^^^^3
2 Calculate it (it's bigger than the number of atoms in the observable universe)
3 Now go back to step 1, this time using the number you just found of up-arrows between the 3s.

Now repeat this entire process 64 times.

can someone tell me what 3^^3 is?

Is it 3^(3^3) ???

Even Moser's number is pretty huge (I'm not sure exactly what it is). It obviously involves Moser's polygon notation, and I think it's something like this: a million inside a million-sided polygon, which is inside that number of that number-sided polygons.

If you don't quite get this, please tell me...

I feel like Euler Avenue is a deserted wasteland... nobody's posted for almost a month here.

Last edited by Laterally Speaking (2007-06-06 22:01:55)

Laterally Speaking wrote:

I feel like Euler Avenue is a deserted wasteland... nobody's posted for almost a month here.

Then the solution is simple - start an interesting and challenging thread of your own. I can offer a host of these, if you want.....

Or are you just a consumer, rather than a producer?