Graham's number

[Kytro]

3^3 means '3 cubed', as it often does in computer printouts.

3^^3 means 3^(3^3), or 3^27, which is already quite large: 3^27 = 7,625,597,484,987, but is still easily written, especially as a tower of 3 numbers: 333.

3^^^3 = 3^^(3^^3), however, is 3^^7,625,597,484,987 = 3^(7,625,597,484,987^7,625,597,484,987), which makes a tower of exponents 7,625,597,484,987 layers high.

3^^^^3 = 3^^^(3^^^3), of course. Even the tower of exponents is now unimaginably large in our usual notation, but Graham's number only starts here.

Consider the number 3^^^...^^^3 in which there are 3^^^^3 arrows. A largish number!

Next construct the number 3^^^...^^^3 where the number of arrows is the previous 3^^^...^^^3 number.

An incredible, ungraspable number! Yet we are only two steps away from the original ginormous 3^^^^3. Now continue this process, making the number of arrows in 3^^^...^^^3 equal to the number at the previous step, until you are 63 steps, yes, sixty-three, steps from 3^^^^3. That is Graham's number.

[WickedLou9]

Note to self... Construct a ridiculously large number based on an illiogcal sequence of exponents. Publish number with my name on it.
Profit.
Lou's number is the same as above just replace 3 with 4.


I'm not sure what the point is of that. It's not like he discovered the number or that it is the biggest number ever constructed. There is no such thing as the biggest number.

[curlyque221]

Math Graduate students, at least where I am, essentially have to make some sort of "discovery" before they complete their program. I bet Graham has his PhD.

[motivez]

I have no idea what this thread is about. Link to something talking about it?

[Kytro]

It is used for Ramsey Theory, see wiki