Defining The Point Range
Regardless if ΔP is infinitesimal or finite, there is (at least—in the case of the derivative—theoretically) a point range, where the boundaries are P ± (.5)ΔP (depending on the orientation—ΔF(P), δF(P) or ∇F(P)):
- LB = Lower Boundary; UB = Upper Boundary;
Derivatives can be regarded as functions themselves, harboring their own derivatives. Thus each function is home to sequential degrees ("higher orders") of derivation, or differentiation. This property can be generalized to all difference quotients.
As this sequencing requires a corresponding boundary splintering, it is practical to break up the point range into smaller, equi-sized sections, with each section being marked by an intermediary point ("Pi"), where LB = P0 and UB = Pń, the nth point, equaling the degree/order:
Read more about this topic: Difference Quotient
Famous quotes containing the words defining the, defining, point and/or range:
“Art, if one employs this term in the broad sense that includes poetry within its realm, is an art of creation laden with ideals, located at the very core of the life of a people, defining the spiritual and moral shape of that life.”
—Ivan Sergeevich Turgenev (1818–1883)
“Art, if one employs this term in the broad sense that includes poetry within its realm, is an art of creation laden with ideals, located at the very core of the life of a people, defining the spiritual and moral shape of that life.”
—Ivan Sergeevich Turgenev (1818–1883)
“The whole point of Camp is to dethrone the serious. Camp is playful, anti-serious. More precisely, Camp involves a new, more complex relation to “the serious.” One can be serious about the frivolous, frivolous about the serious.”
—Susan Sontag (b. 1933)
“Whereas children can learn from their interactions with their parents how to get along in one sort of social hierarchy—that of the family—it is from their interactions with peers that they can best learn how to survive among equals in a wide range of social situations.”
—Zick Rubin (20th century)