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> Depends on what you mean by “expressed”

I'll have to think about this. I want a very physical meaning of the term using values rather than references. One where the largest number that can be expressed using up/down fingers with two hands is 1024, not a sign language reference to a googolplex.




If you are OK with a sum constants times powers of two, would you be ok with other hyperoperations on two?

https://en.m.wikipedia.org/wiki/Hyperoperation

I wonder if it would be helpful to restrict the question a bit, maybe something like: what is the largest number for which the number, and also all smaller magnitude integers, can be expressed.


You might enjoy:

"Measuring the intelligence of an idealized mechanical knowing agent" https://philpapers.org/archive/ALEMTI-2.pdf

"Intuitive Ordinal Notations" https://github.com/semitrivial/IONs


all expression is reference




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