Preliminary investigations on induction over real numbers
Gilles Dowek (LOGICAL)

TL;DR
This paper introduces a novel induction principle applicable to real numbers, extending the classical natural number induction to a continuous domain, which could impact analysis and related fields.
Contribution
It proposes a new induction principle for real numbers, filling a gap in the theoretical framework for reasoning over continuous domains.
Findings
Formulated a real number induction principle
Established theoretical foundations for real induction
Potential applications in analysis and formal verification
Abstract
The induction principle for natural numbers expresses that when a property holds for some natural number a and is hereditary, then it holds for all numbers greater than or equal to a. We present a similar principle for real numbers.
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.
Taxonomy
TopicsComputability, Logic, AI Algorithms
