Numbers and numerosities

TL;DR

This paper advances the theory of numerosity by exploring its connections with various types of numbers, including ordinals, cardinals, hyperreals, and surreals, and proposes a unified continuum concept.

Contribution

It introduces a new framework linking numerosity with continuum and infinite number sets, integrating multiple number systems into a cohesive theory.

Findings

Unified continuum definition encompassing various infinite number sets

New insights into the relationship between numerosity and different number types

Enhanced understanding of the Euclidean line in the context of infinite sets

Abstract

We develop new aspects of the the of numerosity theory; more exactly, we emphasize its relation with the ordinal numbers, cardinal numbers, hyperreal numbers and surreal numbers. In particular, we combine the notion of numerosity with the idea of continuum and we get a definition of Euclidean line which includes all the sets of infinite numbers mentioned above.