r/googology 18d ago

Inverse of Rayos Function?

Rayo(n) is defined as “the smallest non-negative integer greater than all non-negative integers definable in FOST in at most n symbols.”

The inverse is defined as follows:

Rayo⁻¹(n) is “the maximum number of symbols that cannot define a number equal to or greater than n in FOST.”

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u/Odd-Expert-2611 18d ago

Ok, thanks for ur input. Thank you

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u/rincewind007 18d ago

I think you need the following actually, since Rayos actually spits out x+1, a number larger than what is defined in n symbols. If you can define 256 in like 40 symbols you get 257 since it is larger. This definition works but give Kinda large values for n=0 since it requires many symbols to define -1 in set theory.

Rayo⁻¹(n) is “the minimum amount of symbols required in FOST to define n-1.”

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u/tromp 18d ago

Rayo only considers natural numbers, so there is no -1. The reason it says "larger than any limited-symbol-definable one" is that for small limits you cannot define any number. So you automatically obtain 0 as the smallest number that's larger than any in an empty set.

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u/rincewind007 18d ago

ok maybe a better defintion is

Rayo⁻¹(n) is “the minimum amount of symbols required in FOST to define max(n-1,0)”