Using Grossone to count the number of elements of infinite sets and the connection with bijections

TL;DR

This paper explores Sergeyev's Grossone numeral system to count elements of infinite sets, examining its relation to bijections and contrasting it with traditional set theory approaches.

Contribution

It introduces a novel method for counting infinite set elements using Grossone and analyzes its implications for bijections and set theory.

Findings

Grossone provides a new way to quantify infinite sets.

The approach differs from traditional naive set theory.

Connections between set cardinality and bijections are reinterpreted.

Abstract

In this paper, we look at how to count the number of elements of a set within the frame of Sergeyev's numeral system. We also look at the connection between the number of elements of a set and the notion of bijection in this new setting. We also show the difference between this new numeral system and the results of the traditional naive set theory.