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2023年4月5日 · From what I have gathered online about these numbers, they say that Loader's Number is larger than TREE(3) or SSCG(3) or similar. The reasoning I have seen goes is that Loader's Number is the largest computable number and TREE(3) and SSCG(3) are ostensibly computable numbers. But how do we know that:

This leads to a sequence of more than tree $_3$ (tree $_2$ (tree(8))) trees. Thus TREE(3) > tree $_3$ (tree $_2$ (tree(8))). As you can imagine, the TREE(n) function clearly outpaces the tree(n) function, which is already at the level of the Small Veblen Ordinal in the fast-growing hierarchy.

2016年8月13日 · No, a number like 10^(10^100) is much smaller than Rayo(10^100), because there are not a Googol digits, but a Googol symbols in first order set-theory, and it is pretty efficient to write down big numbers such as TREE(3), which can be expressed with MUCH LESS than a Googol symbols, you don't need anything like a Googol symbols to express TREE(3 ...

2023年10月19日 · $\begingroup$ Thanks for the link Benjamin! On the one hand, it appears that this is a very difficult question, yet on the other hand, Friedman writes, "Also, numbers derived from Goodstein sequences or Paris/Harrington Ramsey theory, although bigger than n(4), are also completely UNNOTICEABLE in comparison to TREE[3]."

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2017年10月28日 · Contrary to r.e.s.'s answer, the restriction to subcubic graphs is not necessary. See here, for example.. It is not hard to prove this:

He mentions a theorem relating SCG(13) to the halting-time of a Turning machine. But I'm asking for an answer expressed (in some manner) in terms of the g(n) notation for large numbers (the notation in which Graham's number is g(64) ), (Paragraph) .Friedman says that, compared to SCG(13), TREE(3) is unnoticeable. So, sure, TREE(3) is a lower bound.

2017年5月21日 · No, Rayo's Number is just too big, imagine a Googol symbols in the first order set theory, you cannot express it, why? because even writing down a symbol per Planck time (5.39 x 10^-44 seconds) it would still take about 10^48 years, and another problem is the space, the number of particles in the observable is about 10^80, a Googol is 10^100,and bigger than …