You CANNOT imagine this number! (Graham's Number)

👉 In this video we look at what energy actually is, and how we can reduce energy to the motion of particles.

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⏱ Timestamps:
00:00 Intro
01:03 1: Standard Notation
01:30 2: Scientific Notation
03:48 3. Factorial Notation
06:23 4. UP-arrow Notation
11:17 5. Stupidly large numbers...
12:00 6. Unimaginable...
13:26 7. The Final Boss

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👍 Thanks for watching!

#LargeNumbers #GrahamsNumber #OnlineEducation

[lilyboo]

And yet these unimaginable numbers are still closer to zero than to infinity, i still can't wrap my head around it.

[pthleigh]

Thankyou! This is the clearest explanation of up-arrow notation I've seen on Youtube. Great job!

[AymanTravelTransport]

Beyond Graham's Number, you'll need transfinite ordinals in the fast-growing hierarchy (diagonalisation of functions to create something faster than any function that can be expressed via strictly finite terms) in order to express how big they are, with the lower bound of TREE(3) being very far into this.

[laxxius]

Graham's Number is probably the most popular super huge number after googolplex, but there are a bunch of numbers larger (however they are not used in any mathematical proof like graham's number).

TREE(3) is another kinda famous number that's bigger than G(64). It wasn't used for a mathematical proof, but it was used in an example for a proof, iirc.
SSCG(3) or SCG(13) is in a similar boat to TREE(3).

Busy Beaver numbers are much larger than all of these, and have to do with uncomputable sequences.
Rayo's Number is the grand champion of all big numbers (well, not really but it's most known)

[icebeartwo]

The largest one is Rayo's Number right?

[sreser]

that's funny i was in bed and listening to the videos and never had herd this one before. My first thought was Grahams number when you started and asked us. of course i had no idea the title of this vid. So yea not all people think of small numbers.

[crazymanyt]

There’s no such thing as g 0 it starts at g1

[shreyasbhatt]

Great video!!!
Ok, there is a little problem defining g(0), this has been discussed in the comment section already. but I might as well add a drop in the ocean.
If we define g(0) equal to 3↑↑↑↑3 then the grahm number is g(63). and if we define g(1) equal to 3↑↑↑↑3 then Grahm number is g(64).

[nikhilbontha]

Simple: 2022 - 2024 = -2. 2022 will be a factor of Graham's number of years ago within eight months.

[martins]

It is g1 that equals 3 ^^^^ 3, not g0, I think…


Otherwise, good video.

[fabioML]

So the number of the atoms that compose the earth is 10^50... and the total atom in the universe is only 10^80?
How can this be possible? 🤔🤔

[xmqcypj]

Tan 90 degree - 1 is the greatest number

[nikhilbontha]

_3(3) is an unnecessarily large factor of Graham's number.

[parkershaw]

Let X=3^^^3, a power tower of 3 with 7.6T layers.

g0=3^^^^3=3^^^3^^^3=3^^^X
a tower with X layers, each layer is another (progressively taller from top down) tower!!!

I have no way to imagine g1, let alone g64!!!!

[pacman]

I think I read on Wikipedia awhile ago, they have figured out the last 16 million digits of G64.

[rspsrzc]

F(1)=3
F(x)=3^f(x-1)
3^^^3=f(f(3))
3^^^^3=f^f(f(3))-1(3)

[SAKURAo]

10:28 is this an error? How does the 3 ↑ ↑4 has the same digits with 3 ↑ ↑3?

[csabafarago]

3↑↑↑↑3 is the first number in the Graham series, not the zeroth.

[gamingxpromax]

tree of grahams number tetrated to tree of grahams number

[nikhilbontha]

Infinity is not a real number, so it'sn't allowed.