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  • Rayo (64)是否比葛立恒数大？ - 知乎
    从 2007 年被 Agustín Rayo 提出以来，「Rayo 数」长时间都被认为是人类创造的增长率最快的函数，2013 年时，日本人 Fish 创造了「Fish number 7」，虽然名义上比 Rayo 数增长更快，但本质只是 Rayo 数的一个概念拓展。
  • Is Rayos number really that big? - Mathematics Stack Exchange
    I was reading about large numbers, and came across Rayo's Number which is defined to be the smallest integer that is not nameable by any expression in the language of set theory that contains less
  • 为什么loader数是可计算的，但是rayo数不可计算？ - 知乎
    为什么loader数是可计算的，但是rayo数不可计算？ 看了一下loader数的定义，感觉和rayo数很像啊，都是“在XX步以内定义的数字中，比最大的数字更大的一个数字”，为啥rayo数是不可数的，但是lo… 显示全部 关注者 15 被浏览
  • How Big would Grahams Tree be? - Mathematics Stack Exchange
    What if in Graham’s Number every “3” was replaced by “tree(3)” instead? How big is this number? Greater than Rayo’s number? Greater than every current named number?
  • 科学领域中目前有意义的最大数字是多少？ - 知乎
    为了避免自我指涉的麻烦，Rayo数选定的是一阶集合论语言这一形式语言，但为此付出的代价就是，Rayo函数（把Rayo数的定义里面的“ 10^ {100} ”换成自变量）不能在一阶集合论语言中定义。 人们对Rayo函数了解得实在太少，还未发现它的一些函数值
  • Showing that Graham Number $G_ {64}$, $TREE (3)$, loader. c output $D . . .
    $\text {Loader's Number} < BB (1015) < BB (2^ {65536}-1) \leq Rayo (7339) < Rayo (10^ {100})$ The proof that $\text {Loader's number} < BB (1015)$ is that "output_loader txt", a $1015$ -state, $2$ -symbol Turing machine written by CatIsFluffy, computes (a slightly larger variant of) Loader's number steps before halting
  • Which is the largest number out of these three$?$
    Now everyone knows that it is the largest number till date But I've heard of some numbers that are even larger than Rayo's Number The two of them are Fish number $7$ and BigFoot I couldn't find their wikipedia so I can't attach their definitions Which number of three of them is the biggest $?$ Also, if someone can explain me the definition of Rayo's Number it would be greatly appreciated
  • If Rayos number construction is not limited to first order set theory . . .
    4 Rayo's number is named by an expression in the language of first order set-theory I wonder if we extend this definition to any higher order logics, will the result significantly change? (because for most (useful) models in higher logic we can still find expression in first order logic) I am not professional in set theory proof theory





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