Tree of Three Number So Large Even Two Trillion Pages Cannot Prove Its Existence

What was said

"You can't prove it exists without using 2 to the 1 trillion pieces of paper. That doesn't mean that it's bigger than 2 to the trillion. It's incredibly bigger than that. Even with 2 trillion pieces of paper, you're not even proving it exists."

The number TREE(3), derived from Kruskal's theorem about infinite sequences of finite trees, is so incomprehensibly large that even with computational resources using 2 to the trillion pages of proof, its existence cannot be demonstrated within standard arithmetic. Graham's number is minuscule by comparison, barely noticeable next to TREE(3).