| 1. | An important application of monotonic functions is in probability theory.
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| 2. | If they are monotonic functions of each other, that is enough.
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| 3. | What is needed is not that they are monotonic functions of their argument.
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| 4. | Temperature is a monotonic function of the average molecular kinetic energy of a substance.
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| 5. | The state progression is a monotonic function.
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| 6. | The class of all preordered sets with monotonic functions as morphisms forms a category, "'Ord " '.
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| 7. | Obviously the variable \ tau can be replaced by any monotonic function, \ tau'= f ( \ tau ).
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| 8. | Each cardinal function is a monotonic function of each of its " natural " or " canonical " variables.
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| 9. | It is relevant that for a system at constant volume and mole numbers, the entropy is a monotonic function of the internal energy.
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| 10. | We can choose any monotonic function for our g ( T ); it is a matter of convenience and convention that we choose g ( T ) = T.
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