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No. The amount of time it takes to write Rayo’s number is 1, in units of Rayotime.
Correct but not the answer we’re looking for.
Ok, then it takes two Planck times if you write it in base Rayo.
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Write it how? Seeing as Rayo’s number is defined as the smallest number bigger than what can be written in first order set theory with a googol symbols, you could probably write down the number with, say, googol+1 symbols. Or let’s just say 2*googol symbols, that should certainly be enough. It would not take Rayo’s number amount of seconds to write down 2 * googol symbols.
TL;DR: No.