The Continuous and the Infinitesimal in Mathematics and Philosophy

19th and Early actual infinite Ancient Greece argument Aristotle arithmetical assertion atomists atoms axiom body Bois-Reymond Brentano Brouwer called Cantor classical composed conceived considered constructive continuous function continuum coordinates corresponding curve Dedekind defined definition derivative determined domain Early 20th Centuries elements Epicurus equal Euler example excluded middle existence extension fact finite follows formulation functor given idea indecomposable indivisible infinite number infinitely divisible infinitely small Infinitesimal Calculus infinity intensive quantities intuition intuitionistic intuitionistic logic Kant law of excluded Leibniz limit logic magnitude manifold mathematical mathematicians matter means microquantities monads motion Mutakallemim natural numbers neighbourhood nonstandard nonstandard analysis object open set philosophers physical possible presheaf principle properties quantities Quoted ibid rational numbers real numbers regarded relation Russell segment sense sequence smooth infinitesimal analysis straight line subsets suppose tangent theorem theory things topological space topos triangle variable Weyl Zeno’s zero