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