The inconsistency of the natural number system
Purpose - The paper aims to use a third method to show that the system of natural numbers is inconsistent. Design/methodology/approach - A conceptual approach is taken. Findings - Without directly employing the concepts of potential and actual infinities, the authors show that the concept of the set N = {x vertical bar n(x)}, where n(x) =(df) "x is a natural number" of all natural numbers is a self-contradicting, incorrect concept. Originality/value - The paper shows the system of natural numbers to be inconsistent.
cybernetics set theory mathematics number theory