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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|n(x)}, where n(x)=def “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.
© Emerald Group Publishing Limited
2008
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