TL;DR
This survey discusses fusible numbers, identifies errors in previous recursive formulas, proposes a new conjecture, and explores their properties and open problems in the field.
Contribution
It corrects a recursive formula for fusible numbers, introduces a new conjecture, and establishes foundational properties while outlining future research directions.
Findings
Identified errors in Erickson's recursive formula
Established basic properties of fusible numbers
Proposed approaches and listed open problems
Abstract
We point out that the recursive formula that appears in Erickson's presentation "Fusible Numbers" is incorrect, and pose an alternate conjecture about the structure of fusible numbers. Although we are unable to solve the conjecture, we succeed in establishing some basic properties of fusible numbers. We suggest some possible approaches to the conjecture, and list further problems in the final chapter.
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Taxonomy
TopicsLogic, programming, and type systems · Computability, Logic, AI Algorithms · Logic, Reasoning, and Knowledge