Infinitesimal

Following the work of Weierstrass, it eventually became common to base calculus on limits instead of infinitesimal quantities, though the subject is still occasionally called "infinitesimal calculus".

Historical Much of the earliest development of the infinitesimal calculus by Newton and Leibniz was formulated using expressions such as infinitesimal number and vanishing quantity.

If α is neither 0 nor then the above figure of the infinitesimal elements shows that the length of an infinitesimal rhumb line on the sphere between latitudes φ; and φ + δφ is a sec α δφ.

Just for the record, the chances of being attacked by a shark are infinitesimal, 1 in 3.75 million.

The letter was an inspiring and robust defense of the concept of “”—that any time we speak of the is one that is infinitesimal from our perspective.

The so-called palliative can only reach infinitesimal number of hungry Nigerians who go to sleep every day without the slightest clue of how and where the next meal will come from.

But then, ministering to the needs of infinitesimal minorities while annulling the freedoms of the rest of us has become rather a habit of progressive governments.

Several states already conduct their elections entirely by mail, and an last month of voting in three such states found that officials identified an infinitesimal amount of potentially fraudulent ballots.

Many Nigerians are in jail in foreign countries over crimes that are too infinitesimal to warrant a jail term. Thousands of Nigerian sojourners have been swallowed by the Mediterranean Sea, while scouting for a greener pasture.

A general approach to solving PDE's uses the symmetry property of differential equations, the continuous infinitesimal transformations of solutions to solutions ( Lie theory ).

A long slit of infinitesimal width which is illuminated by light diffracts the light into a series of circular waves and the wavefront which emerges from the slit is a cylindrical wave of uniform intensity.

Also every hyperreal that is not infinitely large will be infinitely close to an ordinary real, in other words, it will be the sum of an ordinary real and an infinitesimal.

Alternative angles A conformal map is called that because it preserves the shapes of things (at an infinitesimal scale).

Any Digimon that receives a fatal wound will dissolve into infinitesimal bits of data.

Because of this, the Principia has been called "a book dense with the theory and application of the infinitesimal calculus" in modern times Clifford Truesdell, Essays in the History of Mechanics (Berlin, 1968), at p.99.

Bernstein and Robinson show that if T is polynomially compact, then there is a hyperfinite index w such that the matrix coefficient a w+1,w is infinitesimal.

Cauchy defined an infinitesimal in Cours d'Analyse (1827) in terms of a sequence tending to zero.

Cauchy defined infinitely small quantities in terms of variable quantities, and his definition of continuity closely parallels the infinitesimal definition used today (see microcontinuity ).

Cauchy gave an explicit definition of an infinitesimal in terms of a sequence tending to zero.

Cavalieri's work was not well respected since his methods could lead to erroneous results, and the infinitesimal quantities he introduced were disreputable at first.