About a virtual subset

TL;DR

This paper introduces a novel approach to set theory using virtual subsets, specifically constructed prime number subsets, to generate the entire prime set and expand theoretical frameworks.

Contribution

It proposes a new concept of virtual subsets in set theory, demonstrated through prime number subsets called prime brother, sisters, and cousins.

Findings

Prime subsets can generate the entire prime set.

Virtual subsets offer a new approach to set theory expansion.

Disjoint prime subsets lead to the concept of isolated primes.

Abstract

Two constructed prime number subsets (called prime brother & sisters and prime cousins) lead to a third one (called isolated primes) so that all three disjoint subsets together generate the prime number set. It should be suggested how the subset of isolated primes give a new approach to expand the set theory by using virtual subsets.