Hatred it "brings a process to completion". <poem>I study hatred with great diligence, For that's a passion in my own control, A sort of besom that can clear the soul Of everything that is not mind or sense."</poem> Hatred Hatred or hate is a human emotion. Hatred could invoke feelings of animosity, anger or resentment, which can be directed against certain individuals, groups, entities, objects, behaviors, concepts, or ideas. Hatred is often associated with feelings of anger, disgust and a disposition towards the source of hostility. As an emotion, hatred can be short-lived or long-lasting. It can be of low intensity
Irrational rotation between the additive and multiplicative notations is the group isomorphism It can be shown that is an isometry. There is a strong distinction in circle rotations that depends on whether is rational or irrational. Rational rotations are less interesting examples of dynamical systems because if formula_4 and formula_5, then formula_6 when formula_7. It can also be shown that formula_8 when formula_9. Irrational rotations form a fundamental example in the theory of dynamical systems. According to the Denjoy theorem, every orientation-preserving -diffeomorphism of the circle with an irrational rotation number is topologically conjugate to . An irrational rotation is a measure-preserving