Preliminary investigations on induction over real numbers

2023/05/24 by Gilles Dowek, Dowek, Gilles
Computer Science · #Computability, Logic, AI Algorithms

paper · pdf · doi:10.48550/arxiv.2305.14803

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.

Related

• The Instructor's Guide to Real Induction
• Implications between Induction Principles for ℕ in Peano Arithmetic
• Induction, Coinduction, and Fixed Points: Intuitions and Tutorial
• Finite Sets and Counting
• Proving the existence of the nth root by induction