The Enormous TREE(3) - Numberphile

TL;DR

TREE(3) is an incredibly large number that surpasses Graham's Number, and it is determined by playing a game of trees with different types of seeds.

Transcript

TONY PADILLA: A very very big number, a super super big number. In fact, it's just an off-the-scale big number, and that's TREE(3). It absolutely puts Graham's Number to shame. I mean, really Graham's Number is effectively zero compared to TREE(3). Let's explain where TREE(3) comes from. Well, It comes from a game of trees. There are three differen... Read More

Key Insights

• 🤯 TREE(3) is a mind-bogglingly large number that surpasses Graham's Number.
• 🌲 The determination of TREE(3) is based on playing a game of trees, where trees are constructed with different types of seeds.
• 👾 The length of the longest game of trees determines the value of TREE(3).
• ❓ TREE(3) is not infinite, but its magnitude is so enormous that it is difficult to fathom.
• 💐 There is no known upper bound for TREE(3), but there is a lower bound that involves Ackermann's Number.
• 🈸 TREE(3) has no practical applications and is primarily a result of mathematical exploration and curiosity.

Questions & Answers

Q: How does TREE(3) compare to Graham's Number?

TREE(3) is significantly larger than Graham's Number. In fact, Graham's Number is considered effectively zero in comparison to TREE(3).

Q: How is TREE(3) calculated?

TREE(3) is determined by playing a game of trees, where trees are built consecutively with a maximum number of seeds allowed. The length of the longest game determines TREE(3).

Q: What are the rules of the game of trees?

The rules of the game state that each tree must have a maximum number of seeds based on its position in the sequence. Additionally, if a tree contains an earlier tree, the entire forest dies.

Q: Is TREE(3) an infinite number?

No, TREE(3) is a finite number. However, it is so incredibly large that it can be considered off the scale and impossible to comprehend.

Summary & Key Takeaways

• TREE(3) is a gigantic number that outshines Graham's Number in terms of size.

• The number is obtained through a game of trees, where trees are built one at a time with different types of seeds.

• The trees must follow certain rules and cannot contain earlier trees within them, which leads to the determination of the length of the longest game.