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Arithmetic on strings

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It seems to be impossible to override arithmetic operators on
strings. One can for example set the __add metamethod, but
it only gets called when at least one of the strings cannot be
coerced to a number. For example:
 getmetatable''.__add = function(x,y) return x..y end
 'a'+'b' --> 'ab', fine
 '1'+'2' --> 3

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