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…

read moreWe apply filters to existing sets to express otherwise inexpressible statements.They effectively allow us to refer to infinitely small or infinitely large sets and conduct mathematical analysis to develop valuable insights.

read moreI feel that continuity is best understood when we consider convergence at different levels of abstraction. While it’s fairly easy to understand the continuity of functions when they’re defined in spaces like R2, with standards like: The left hand limit must equal…

read moreI’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…

read moreA discontinuity is any point on a function where one of the three possibilities arise: The right-side limit is unequal to left-side limit The function jumps suddenly The function goes to infinity at a certain point in the domain.

read moreContinuity and limits, as understood in traditional calculus, rely on infinitesimally small sets to arrive at limits for arbitrary functions. This idea, when translated into other definitions of continuities, relies on ideas about convergence of sequences and the like.

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