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Karl comments on Formulas of arithmetic that behave like decision agents - Less Wrong
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I'm confused. What's the distinction between x and
here?
Briefly,
is a variable, while 
is a numeral — i.e., the string 
where 
occurs x times. I just learned that the standard notation is not 
but 
.
Less briefly: As I say in this comment, when I write)
, what I really ought to write is ))
, where )
interprets z as the Gödel number of a string of symbols and replaces every occurrence of the first free variable with the string 1+...+1, where 1 occurs x times.