I remind that I defined generalized limit of arbitrary function. The limit may be an infinitely big value. It allows to define derivative and integral of an arbitrary function. I also defined what are solutions of partial differential equations where such infinities…

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I’ve published a new edition of my book Algebraic General Topology. The new edition features “unfixed morphisms” a way to turn a category into a semigroup. (Certain additional structure on the category is needed.) The book features a wide generalization of general…

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Abstract. A review of my book “Generalized limit (of arbitrary discontinuous function)”. A popular introduction with graphs to the following topic: I consider (a generalized) limit of an arbitrary (discontinuous) function, defined in terms of funcoids. The definition of the generalized limit…

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Traditional calculus as first considered in 17th century by Isaac Newton (and Leibniz, however some say Leibniz stole the Newton’s idea) and then 150 years later formalized (formulated correctly) by Cauchy and Weierstrass, uses limits. Initially calculus was called “infinitesimal calculus”, but…

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Continuing my research from general topology monograph Algebraic General Topology, the following new open problems arose: I remind that I define generalized limit of arbitrary function. This limit is defined in terms of funcoids. As I show in the Book 3, Algebra,…

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Continuing this blog post: The set of all pointfree funcoids on upper semilattices with least elements is exactly a certain algebraic structure defined by propositional formulas. Really just add the identities defining a pointfree funcoid to the identities of an upper semilattice…

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