Internal Set Theory and an Intuitive Development of the Calculus
نویسنده
چکیده
In this paper, we present Internal Set Theory (IST) as a means to more intuitively develop mathematics while still maintaining complete rigor. We begin by stating the axioms of IST and demonstrating several of their central consequences. We then use these results to rigorously introduce the notions of infinitesimal numbers and infinite closeness. Lastly, we develop the calculus in a nonstandard fashion based on these intuitive notions.
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