This is a review of genesis of „ε-δ" language in works of mathematicians of the 19th century. It shows that although the symbols ε and δ were initially introduced in 1823 by Cauchy, no functional relationship for δ as a function of ε was ever ever specified by Cauchy. It was only in 1861 that the epsilon-delta method manifested itself to the full in Weierstrass de_nition of a limit. The article gives various interpretations of these issues later provided by mathematicians. This article presents...
The notion of the number line was formed in 20th century. We consider the generation of this concept in works by M. Stifel (1544), Galileo (1633), Euler (1748), Lambert (1766), Bolzano (1830-1834), M´eray (1869–1872), Cantor (1872), Dedekind (1872), Heine (1872) and Weierstrass (1861-1885).
The paper is devoted to a story of the well-known Rolle's theorem: If the function is continuous on [a, b], differentiable in (a, b) and f (a) = f (b), then there exists in (a, b ) at least one point c such that f'(c) = 0. A history of the associated statements about the roots of a continuous function: If the function f is continuous on [a, b] and has different signs at the ends of the interval, then in (a, b) there is at least one point c such that f (c) = 0. This theorem in the twentieth...
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