Versuch einer Classification der willkürlichen Functionen reeller Argumente nach ihren Aenderungen in den kleinsten Intervallen¶
Du Bois-Reymond, P. (1875). Versuch einer Classification der willkürlichen Functionen reeller Argumente nach ihren Aenderungen in den kleinsten Intervallen. Journal für die reine und angewandte Mathematik.
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2 citations across 2 artifacts.
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Primes¶
- Completeness
- Weierstrass (1872 lectures) consolidated sequential-completeness reasoning in real analysis through his rigorous treatment of continuity, limits, and his celebrated construction of a continuous nowhere-differentiable function.
This sourceConstruction of a continuous nowhere-differentiable function (W(x) = Σ aⁿ cos(bⁿπx) for suitable a, b), published in du Bois-Reymond, P. (1875), "Versuch einer Classification der willkürlichen Functionen reeller Argumente nach ihren Aenderungen in den kleinsten Intervallen", Journal für die reine und angewandte Mathematik, 79, 21–37. Consolidates sequential-completeness reasoning in real analysis through a rigorous treatment of continuity and limits, decisively separating continuity from differentiability.
- Weierstrass (1872 lectures) consolidated sequential-completeness reasoning in real analysis through his rigorous treatment of continuity, limits, and his celebrated construction of a continuous nowhere-differentiable function.
- Infinity
- and Weierstrass (1872)
This sourceThe construction of a continuous nowhere-differentiable function (`W(x) = Σ aⁿ cos(bⁿπx)` for suitable `a, b`), presented in his Berlin lectures; published in Du Bois-Reymond, P. (1875), "Versuch einer Classification der willkürlichen Functionen reeller Argumente nach ihren Aenderungen in den kleinsten Intervallen," Journal für die reine und angewandte Mathematik, 79, 21–37. (Originating treatment of a continuous-everywhere / differentiable-nowhere function, decisively separating continuity from differentiability; also the source of the modern epsilon-delta formulation of continuity that became textbook standard.)
- and Weierstrass (1872)
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