@user81124477516752: IA IA IA IA The Graham’s number is one of the largest numbers ever used in a serious mathematical proof. It is so enormous that it cannot be written down completely, even if you filled the entire universe with paper, screens, or atoms. To get an idea of its size: one million is (10^6), a googol is (10^{100}) (a 1 followed by 100 zeros), and a googolplex is (10^{10^{100}}), which is vastly larger. Even so, Graham’s number is unimaginably bigger than a googolplex. It is defined using the up-arrow notation created by Donald Knuth. For example, (3 \uparrow 3 = 3^3 = 27), (3 \uparrow\uparrow 3 = 3^{27}), which is already enormous, and (3 \uparrow\uparrow\uparrow 3) is far larger. The more arrows you add, the faster the number grows. Graham’s number is built in 64 steps. The first number, (G_1), already uses an enormous number of arrows between two 3s. Then (G_2) uses (G_1) as the number of arrows, (G_3) uses (G_2), and so on until (G_{64}), which is Graham’s number. Although it is unimaginably large, it is not infinite. It is a finite number, meaning it has a last digit, you can add 1 to it to get another number, and it is still much smaller than infinity. For comparison, the observable universe is estimated to contain about (10^{80}) atoms. However, Graham’s number is so huge that not even the number of digits it contains could be written using all the atoms in the universe. A fascinating fact is that, even though we cannot write the entire number, we do know its last digit: it ends in 7. It is one of the best examples of how mathematics can define numbers that are far larger than anything that could ever be physically represented. #targetaudience #ER2014 #fyp #core #lonlieness

elliottcumlicker 💦 :

ELLIOT MENTIONED.💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗💗

tokativ_ :

elliot looked fucking great in this pic holy 😳

aytuco :

Im so lonely I want to go back to school just to see people even though I hate it

user :

this reality is so unfair

nikcruz :

I lov this account sm

malik :

can't relate

Salvatore :

realest

user64530331672 :

saint ER

elliottcumlicker 💦 :

i love elliot smmmmm 💗

🥀cosmin999🥀 :

nikcruz :

real

14basedwaffen88_ :

and then when I try to express how I feel I'm shut down 😭

￴ ￴ ￴ ￴￴ ￴ ￴ ￴ ￴ ￴￴ ￴ ￴ ￴￴ :

Sleep at 6 or 5 am and wake up at 3 pm or 4 pm 1 pm if I’m lucky

nyacoffeeland :

I don’t understand why most of the videos i see have the Grahams number in the caption explained