# The Enormous TREE(3) – Numberphile

Professor Tony Padilla on the epic number, TREE(3). Continues at: https://youtu.be/IihcNa9YAPk

More links & stuff in full description below ↓↓↓

Graham’s Number: http://bit.ly/G_Number

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Some good additional reading on Tree(3):

TREE(3) and impartial games

https://en.wikipedia.org/wiki/Kruskal%27s_tree_theorem

https://mathoverflow.net/questions/93828/how-large-is-tree3

Don't miss the extra footage – Tony says it is better than the main video: https://youtu.be/IihcNa9YAPk

I like how he already sounds tired of its bigness as he goes to draw the very first tree of it at 6:15

This is just racist.

TREE(TREE(3))

There are infinity numbers bigger than tree(3).

Tree(3) is just as far away from infinity as 0 is.

If its soooo big, then post an example with some very large number of trees so us the regulars can visualize it.

ok, now do the TREE(4)

interesting, but you could have at least explained the ackerman function. It's not complicated and the video does not illustrate at all how big it is

3.86×10^92837375838282737344646327282820404049585857574838383828338338383^10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000!^TREE(3)^Googolplex!!!

999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999

if you're colorblind the number is not nearly as large

It's irritating that they never say what TREE (3) is equivalent too!

Tree(tree(3))

What about

TREE(TREE(3))

Hahahhahahahaah

Is Tree(3) greater than googol, or even greater than googolplex?

Edit: i hadn't watched the Video on graham's number before i commented this

So if we know tree(3) is finite, is the tree function of ANY finite number finite? Or is like, tree(Graham) infinite?

I'm not sure I understand the rules. For TREE(2), could you not do (red, green) (green, green) (red red) (green) (red)?

TREE(3) = a, TREE(a)=b … TREE(z) = A … TREE (Z) = ? 😀

Tree 3 lower bound: {100, 100 [ 1 [ 2 1, 2 gun symbol 2] 2] 2}

this is beaf or ban…

What about TREE(TREE(3))?

How about Four Thor?

The largest number that can be expressed in the language of set theory with a {(Tree[(Tree(Tree(Tree……(loaders number times) (Loaders Number)…] to the Loaders Number x Grahams Number arrows)} symbols or less.

You have one point

You keep on expanding the dots into 2 other points. You do this infinitely until the points no longer exist. What is this number?

What about tree pi? Is this where pi is located in? Or e?

A bigger number: TREE(G64)

What about tree(tree(tree(3)))?

is having a 3rd color's purpose is mainly having a different colored 1rst member of the sequence? If so, could that imply that (TREE(4) – TREE(3)) < (TREE(3) – TREE(2))?

OK i am confused, how could this be a finite if a single seed can have almost infinite branches, or is there a upper bound of how many branches a single seed could have? Please somebody could explain.

How do we know it's not infinite?

I wonder why Tree(3) isn't called Gabe Newell's number.

How about TREE(Graham’s Number)

In the example at 6:37 it looks to me like the eighth tree is contained in the seventh tree, and that the tenth tree is contained in the ninth tree. The eleventh tree looks to be contained in a few previous trees. Am I missing something?

But what if… TREE(G64)

When you play the game of trees, you win or you die.

I might be mistaken, but I think Tree(3) is actually off the scales.

I would just like to say I can't see the forest anymore.

I love how "tree" is a mathematical function. 🙂

The size of a tree(3) number of Planck volumes is unimaginably larger than if the entire observable universe were Graham's number times wider

Tree(G64)?

I say it's infinite because you can always keep adding seeds, or to be exact is as big as you want it to be, or they didn't explained it properly

isn't this the equivalent of having 3 primary colors?

Can we somehow use probability to find the last digit of tree(3)

You know its big when you can treat it like infinity.

I still must not understand the problem, because just looking at the continuation at 6:38, why wouldn't it be infinite? You could just keep adding one branch to a seed.

Oh yeah guys? How about tree(tree(3)) got em

It seems that TREE(3) is, for all intents and purposes, basically infinite when it comes to our possible understanding. This means that if you were to play this game with three different seeds, the game would essentially last forever.

This is a shtupidly crazy forest.