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  2. Infinitesimal - Wikipedia

    en.wikipedia.org/wiki/Infinitesimal

    In mathematics, an infinitesimal number is a non-zero quantity that is closer to 0 than any non-zero real number is. The word infinitesimal comes from a 17th-century Modern Latin coinage infinitesimus , which originally referred to the " infinity - eth " item in a sequence .

  3. Category:Mathematics of infinitesimals - Wikipedia

    en.wikipedia.org/wiki/Category:Mathematics_of...

    Download QR code; Print/export Download as PDF; Printable version; In other projects Wikimedia Commons; ... Infinitesimal transformation; L. Laplacian of the indicator;

  4. Infinitesimal character - Wikipedia

    en.wikipedia.org/wiki/Infinitesimal_character

    The infinitesimal character is the linear form on the center of the universal enveloping algebra of the Lie algebra of that the representation induces. This construction relies on some extended version of Schur's lemma to show that any z {\displaystyle z} in Z {\displaystyle Z} acts on V {\displaystyle V} as a scalar, which by abuse of notation ...

  5. Increment theorem - Wikipedia

    en.wikipedia.org/wiki/Increment_theorem

    In nonstandard analysis, a field of mathematics, the increment theorem states the following: Suppose a function y = f(x) is differentiable at x and that Δx is infinitesimal. Then Δ y = f ′ ( x ) Δ x + ε Δ x {\displaystyle \Delta y=f'(x)\,\Delta x+\varepsilon \,\Delta x} for some infinitesimal ε , where Δ y = f ( x + Δ x ) − f ( x ...

  6. Nonstandard analysis - Wikipedia

    en.wikipedia.org/wiki/Nonstandard_analysis

    A hyperreal r is infinitesimal if and only if it is infinitely close to 0. For example, if n is a hyperinteger, i.e. an element of *N − N, then 1/n is an infinitesimal. A hyperreal r is limited (or finite) if and only if its absolute value is dominated by (less than) a standard integer.

  7. Howard Jerome Keisler - Wikipedia

    en.wikipedia.org/wiki/Howard_Jerome_Keisler

    Howard Jerome Keisler (born 3 December 1936) is an American mathematician, currently professor emeritus at University of Wisconsin–Madison.His research has included model theory and non-standard analysis.

  8. Infinity - Wikipedia

    en.wikipedia.org/wiki/Infinity

    In 1655, John Wallis first used the notation for such a number in his De sectionibus conicis, [19] and exploited it in area calculations by dividing the region into infinitesimal strips of width on the order of . [20] But in Arithmetica infinitorum (1656), [21] he indicates infinite series, infinite products and infinite continued fractions by ...

  9. Mathematical manuscripts of Karl Marx - Wikipedia

    en.wikipedia.org/wiki/Mathematical_manuscripts...

    Marx left over 1000 manuscript pages [3] of mathematical notes on his attempts at discovering the foundations of calculus. The majority of these manuscript pages have been collected into four papers, along with drafts and supplementary notes in the published editions of his collected works. [4]