Dear Prof. Nicolas, I attach as an official submission to Publications mathématiques de l’IHÉS my breakthrough article which defines a generalization of the well known concept of limit from analysis and general topology. Please inform as the review goes. limit.pdf Next day…
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Differential and integral calculus are two of the most important mathematical discoveries of the last few centuries. Since the work of Isaac Newton in 1665, through Lagrange and Cauchy, to formalize this branch of mathematics—calculus has served a crucial role in most…
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Calculus has served a crucial role in most fields of human inquiry. Anyone who’s done even basic geometry and algebra would appreciate the importance of calculus. Learn more about calculus here:
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One of the fields of human inquiry that make extensive use of mathematics and calculus is economics. Contemporary economic theory relies heavily on mathematical concepts and ideas to make sense or and theorize about economic phenomenon to devise economic models/policies. Anyone who…
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Topological continuity is a key concept within mathematical theory. Topological analysis has opened paths to a deeper understanding of continuity at a more abstract level. However, topological continuity isn’t the only form of continuity mathematicians study—discrete continuity is one type of continuity…
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We 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.
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I 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…
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A 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.
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Continuity 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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