What is the information content of a sentence S like 'one has a successor'. To me, it looks like if we assume no a priori knowledge, both S and it's negation will have equal probablity 1/2. This is to say that one could work with S as an axiom or equally with its negation as an axiom. In a real world parallel, the situation could be of a calculator that overflows at 1+1 and another which does not.So the information content of S would appear to be just One unit. With that reasoning ,the information content of sentence U 'Every number has a successor' would be infinite,or an associated probability of 0. Is it that it would be inappropriate to speak of information content of a mathematical axiom like S or U above?
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