It’s a principle that provides the basic and the essential part in the mathematics of sorting and even counting. This principle was introduced by Johann Peter Gustav Lejeune Dirichlet in 1834. He called it the shelf principle or drawer principle. However, many people appreciate his insight and call it the Dirichlet drawer principle. The name pigeonhole was introduced in 1940 by Raphael Robinson. In the literal sense, pigeonholes refer to shelves or holes used to place pigeons. Thus, the principle roughly states that if one has a given number of boxes and a given number of items to ...
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Karl Theodor Wilhelm Weierstrass was a German mathematician who is often called as the "father of modern analysis".
Weierstrass was interested in the soundness of calculus, and also made significant advancements in the field of calculus of variations. Among the several significant axioms, Weierstrass established a necessary condition for the existence of strong extrema of variational problems. As we know, Cauchy gave a form of the (ε, δ)-definition of limit, in the context of formally defining the derivative, in the 1820s, but did not correctly distinguish between continuity at a point versus uniform continuity on an interval, due to insufficient rigor. Notably, in his 1821 Cours d'analyse, Cauchy gave a famously incorrect proof that the (pointwise) limit of (pointwise) continuous functions was ...
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