Collective Property of Numbers and Its Mathematical Refutation

TL;DR

This paper proves that the set of numbers with the 'collective' property, defined as being the greatest lower bound of a bounded, strictly decreasing sequence, is empty, clarifying a fundamental aspect of real numbers.

Contribution

It provides a mathematical refutation showing that no real number possesses the 'collective' property, resolving a previously unclear aspect of number properties.

Findings

Numbers with the collective property form an empty set.

The collective property cannot be satisfied by any real number.

This refutes any assumptions of the existence of such numbers.

Abstract

A number has the "collective" property if the number is the greatest lower bound of a bounded, strictly decreasing sequence on the real line. We prove that numbers with the collective property constitute an empty set.