Versuch einer Classification der willkürlichen Functionen reeller Argumente nach ihren Aenderungen in den kleinsten Intervallen¶
Weierstrass, K. (1872). 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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