The largest number yet… a tree.

Honestly, three trees are way larger than graham’s number.

All the information provided is from Numberphile, again.

TREE(3).

Remember Graham’s Number? Well, this TREE(3) is so large, Graham’s Number will look tiny. Miniscule.

It all starts from a game that looks fun.

You know trees? No, not nature. Mathematical trees.

Kinda.

Let’s play a game. Choose a small number. Let’s start with one colour, #FF620E. For the curious ones, that’s an orangey colour. Draw a dot. First rule!

The trees, at their levels, if it is level n, then it can only have up to n dots. Understandable. Second rule!

If a previous tree is contained in a new tree, the whole “forest” of trees die. What?

A treeling.

This tree. It is directly contained in the tree above, the full alphabet tree, and therefore the trees die. Forest burning… wow.

New example!

Is this tree:

Nice tree

Contained in this tree?

VERY NICE.

No. REWORDING TIME! If two trees with two equivalent dots share a COMMON ancestor, then the game dies and deforestation is carried out. So, in the above trees, the two dots are the same, but its common ancestor is not the same, so no deforestation. #stopdeforestation

Now. Is this tree:

The same tree.

Contained in this tree?

Like, the BEST tree.

Yes. The two black dots share a COMMON ancestor, a yellow dot, therefore the first tree is contained in the second tree, and deforestation carries on.

So. the TREE function. TREE(1). How long could you go in this game before you have to stop? 1. #FF620E seed, all by itself. How many for two seeds, TREE(2)? The new colour is #000000, or black.

TREE(2) = 3.

You can’t do more than this.

What’s the next step? TREE(3).

If you started from the Big Bang, according to Numberphile, you wouldn’t be able to finish before the universe ended. It’s that large.

But there’s more. Next step: SSCG(3)

But that’s for next time.

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