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  text: 'Mathematics is the study of crisply specified formal objects — for example, [number numbers] — and the ways of knowing their [mathematical_properties properties] — such as [-proofs].  We can see "[-258]" as the study of "which conclusions follow with certainty from which premises".  Using this definition of logic, we can also see mathematics as the study of logical objects in logical universes — entities whose properties follow from specifications about them, rather than from observation of the real world.  The number 3 is a logical object because its behavior follows from axioms about addition and multiplication; Mount Everest is a physical object because we learn about it by physically measuring Mount Everest.',
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