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The write-up manages to misquote Rayo's huge entry "The smallest number bigger than any finite number named by an expression in the language of set theory with
by tromp 10y ago
The write-up manages to misquote Rayo's huge entry
"The smallest number bigger than any finite number named by an expression in the language of set theory with a googol symbols or less"
into the relatively minute
"The least number that cannot be uniquely described by an expression of first-order set theory that contains no more than a googol (10^100) symbols."
by leaving out the crucial "bigger than".
The latter is no more than #symbols ^ googol
since any N descriptions cannot describe all of the first N+1 numbers...
Similarly, the proposed function F(n) is merely exponential in n.
- codeflo 10y agoI think you're correct. For the same reason, the proposed "more quickly" growing G(n) is bounded by (constant + n)^n, which is not much of an improvement.
- ggchappell 10y agoThe post takes comments. Write one?
- tromp 10y agoThanks for pointing that out. Awaiting moderation... (the lack thereof makes HN's commenting much more satisfying:-)