TL;DR
This paper introduces a formal framework called Darboux Calculus for analyzing partially defined functions between ordered sets, unifying key concepts in elementary real analysis such as Dedekind cuts, limits, and continuity.
Contribution
It provides a uniform, conceptual approach to fundamental real analysis concepts through a new formalism for partially defined functions.
Findings
Unified framework for real analysis concepts
Simplifies understanding of limits and continuity
Connects Dedekind cuts with function analysis
Abstract
We introduce a formalism to analyze partially defined functions between ordered sets. We show that our construction provides a uniform and conceptual approach to all the main definitions encountered in elementary real analysis including Dedekind cuts, limits and continuity.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.