Too construct this number you first take the number 9 and place a single arrow next to it like this 9↑ you then place another 9 next to the arrow like so 9↑9 this means 9^9 or 9 multiplied by itself 9 times. We then take two arrows this looks like this 9↑↑9 this means 9 stack 9 or a power tower containing 9 9's. We then apply the triple up arrow to the previous number So that it looks like this 9↑↑↑9 this could also be written as 9↑↑9↑↑9 or a power tower containing 9↑↑9 number of 9's. We then then do the quadruple up arrow operation on that number once we've got that number we apply the pental arrow operation on that number or the 5 up arrow operation. We continue doing this process until we have reach the 9↑(9) 9th stage of the process of generating this number but be warned to get to calculate the full decimal expansion of the numbers in the final stages you have to have a computer the size of the universe just to hold all of the data. But of course like all ridiculously huge numbers when it seems like its the end its just the beginning you then take the previous number I mentioned and place that many arrows between the two nines making an even bigger number we call this S1 or Super 1 We then take S1 and put that many arrows in between the 9's and call the S2 we repeat this process until we have done it 9↑(9)9 times the 9 in the brackets represents 9 up arrows.
All though the definition of this number may seem very similar to that of the Graham-Gardner number it really isn't as the definition of the Super number has nothing to do with the N dimensional cubes.
So there you go the super number.