Modulus of Continuity of Higher Orders
It can be seen that formal definition of the modulus uses notion of finite difference of first order:
If we replace that difference with a difference of order n we get a modulus of continuity of order n:
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Famous quotes containing the words continuity, higher and/or orders:
“There is never a beginning, there is never an end, to the inexplicable continuity of this web of God, but always circular power returning into itself.”
—Ralph Waldo Emerson (1803–1882)
“Le Corbusier was the sort of relentlessly rational intellectual that only France loves wholeheartedly, the logician who flies higher and higher in ever-decreasing circles until, with one last, utterly inevitable induction, he disappears up his own fundamental aperture and emerges in the fourth dimension as a needle-thin umber bird.”
—Tom Wolfe (b. 1931)
“One cannot be a good historian of the outward, visible world without giving some thought to the hidden, private life of ordinary people; and on the other hand one cannot be a good historian of this inner life without taking into account outward events where these are relevant. They are two orders of fact which reflect each other, which are always linked and which sometimes provoke each other.”
—Victor Hugo (1802–1885)