Infinity Explorer

Exploring Different Forms of Infinities and Their Implications

Overview

This project is dedicated to the exploration and understanding of various aspects of infinity in mathematics. It collects notes on Cantor's diagonalization argument, the study of countable and uncountable sets, and other related mathematical problems.

Contents

• Introduction to Infinity: Concepts of countable and uncountable infinities.
• Cantor's Diagonalization: Proof and code implementation.
• Cardinality and Aleph Numbers: Exploring the sizes of infinite sets.
• Power Sets: Understanding the implications of Cantor's theorem on power sets.
• Applications in Logic and Computer Science: Gödel's Incompleteness Theorems, Turing's Halting Problem, and complexity theory.
• Code Examples: Practical examples and implementations in Rust.

Status

This repository is an evolving set of notes and small experiments. It currently collects the conceptual overview and outline above. Code implementations, including the Rust examples for Cantor's diagonalization and related arguments, are planned and in progress, so there is no src/ directory to build yet.

To follow along or clone the repository:

git clone https://github.com/iteba15/Infinity-explorer.git
cd Infinity-explorer

Author

Allan Kiplagat Iteba (GitHub @iteba15), BSc Astrophysics & Space Science, University of Nairobi.

• LinkedIn: (link to be added)
• ResearchGate: (link to be added)