For example, how to prove that TREE(n) for an extremely large n, like TREE(TREE(3)) is finite, in layman’s terms? Or is it impossible to understand the proof without being an expert in graph theory?
In: Mathematics
In general, anything that can be broken down into simple, solvable arithmetic operations is *always* finite. All TREE(n) is doing is a lot of exponent operations. If you put in a finite number, you always get a finite number out of them. That number can be ridiculously large, but it’s finite.
We get infinities in math when we start dealing with things like dividing by a number that gets closer and closer and closer to zero. Those are not simple arithmetic.
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