Giant numbers

A guide to very very big numbers. This video covers googol, tetration, hyperoperations, Graham's number and TREE(3). Enjoy!

[RandomAndgit]

Several quick notes:
Yes, I am aware of SSCG(3) and Rayo's number but I thought that the video would drag on a little.
There are several minor errors with the visuals. Specifically at 3:19 where it says that 65536 is 2 tetrated to 5 rather than 2 tetrated to 4 and at 6:31 where it shows TREE(10^10) when I say "TREE(googol)" when it should show TREE(10^100)
When talking about graham's number, I said that g0 was 3 hexated to 3 but actually that's g1 and g0 isn't really a thing.
I excluded infinity because I intend to make another video covering exclusively infinities.
At 4:56 I display G↑ᴳ but, in actuality, this is an incomplete equation because you need another number on the other side of the equation. I basically just wrote the equivalent of "5 +" without a second number.
Sorry about the music being a little too loud.

Edit: Yes, everyone. I am writing a script for a sequel. You can stop mentioning SSCG(3), Rayo's number, BIG FOOT, the fast-growing hierarchy, etc...

[whentheskittlesfightback]

"hey you want TREE(3) chips"
"what"
and then they were crushed under the unfathomable mass of an impossible number of chips

[oboo]

"we cannot meet giants, but we may glimpse them on the horizon, and bask in their radiance" is such a fire line

[fawfulfan]

To try to wrap your head around how fast TREE grows: what do you think is larger, G(TREE(3)), or TREE(4)? The answer is TREE(4) and it's not even close.

[magicmulder]

The funniest part about TREE(3) is that the first color is “burnt” after the first tree and you build the entire rest with two colors only.

[gameplaysh]

You may have science on your side, but you'll never beat that one kid at the playground.

[qwarty_gd]

Remember, every giant number in this video is closer to 0 than it is closer to infinity

[noob-rusc]

the hospital's bill after they told me to drink more water:

[Anriokk]

-Hello! Can I have f_10(10(↑10)10) Bottles of water, please.

-Man, what are you talking about...

[AndrewHorsford]

The thing that always sticks in my throat with these numbers is that for Graham's Number we can see how it's constructed and why it's so large, but Tree(3) et al are described as "omg like, big... you can't even..." without any attempt to ever SHOW with even a hand-waving attempt at the operations used to BEGIN the climb to it.

[kylebroussard]

*The mathematicians version of "whatever you said times 1 billion"*

Edit: to be fair, the name of this video was "The Biggest Number" or something like that when I made this comment.

[lawaataling]

Could I have TREE(3) croissants, please? Keep the change

[Ioz_Wake_Up]

5:35 I love the way he says TREE so violently. As if it was a prequel to his explaination of this crazy ass number

[ToiletCL]

The fact that there are more possible chess combinations than atoms in the universe just blows my mind.

[Audisknfj]

Rayo’s number gets mentioned a lot here, and I would like to bring up some fun properties of Rayo’s function used to construct such number

The function grows linearly when the input value is small: with 10 first order set theory symbols you can write 1, with 30 you can write 2. Seems slow right?

This is not the case however as it grows faster. By 300 you have the function growing at the rate of multiplication, by 340 you have it grow at the rate of exponentiation, and by 400 the rate becomes tetration. And we’re not talking about the actual value of Rayo’s function; no, this is just a lower bound. If I remember correctly, RAYO(380) is at least greater than 2^65536

By the time you reach 7400, Rayo’s function grows so fast that it is almost certainly possible that the value is greater than S(2^65536-1), S() is a function that is growing faster than ANY COMPUTABLE FUNCTION, faster than G, faster than Tree, and so on

And Rayo’s number has the input set at a googol. The number would certainly be so big that the number would not only lose its meaning, but any number or symbols or machines that can enclose an iota of its being will certainly collapse into a black hole, for there isn’t close to enough information to store the concept of Rayo’s number

[FormallyKnownedAsKardboard]

“Hey look, theres a TREE(3)”
Tree?, i dont see any trees
“no, TREE(3)”
ohhhh.

[tomaszsmoter]

"hey, you want some 5 pentated to 5 chips?"
"man, what is wrong with you."
*dies of major pressure under the unimaginable mass of an unfathomable amount of chips*

[joshuaguzman]

5:04 when i heard lets draw some trees i knew it was over

[Minecraft]

Fun fact: when i was sick, i had a nightmare of dividing, subtracting, multiplying, adding numbers at the same time

[realwaterenderman]

McDonalds in a nutshell:
"No pickles please"
"Alright!"
"Here's your burger sir!"
"WHY DID YOU PUT TREE(TREE(TREE(10^100))) TETRATED PICKLES ON IT"
"That'll be $Weakly Compact Cardinal"