Role
The main role of the tangent bundle is to provide a domain and range for the derivative of a smooth function. Namely, if is a smooth function, with and smooth manifolds, its derivative is a smooth function .
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Famous quotes containing the word role:
“Totalitarianism is never content to rule by external means, namely, through the state and a machinery of violence; thanks to its peculiar ideology and the role assigned to it in this apparatus of coercion, totalitarianism has discovered a means of dominating and terrorizing human beings from within.”
—Hannah Arendt (1906–1975)
“The Declaration [of Independence] was not a protest against government, but against the excess of government. It prescribed the proper role of government, to secure the rights of individuals and to effect their safety and happiness. In modern society, no individual can do this alone. So government is not a necessary evil but a necessary good.”
—Gerald R. Ford (b. 1913)
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—Joan Sheingold Ditzion and Dennie Palmer (20th century)