Exercise · ZW-CONSTRUCTION-OF-THE-NATURALS-010 · ★★★ Advanced

Which statement gives a counterexample to the claim that \(n^+=n\) for every natural \(n\)?

Choose one option.

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  • A. For \(n=0\), \(0^+=\{0\}\ne\varnothing=0\), so \(n^+\ne n\) there

Explanation

Zero differs from its successor, since \(\{0\}\) has one element and the empty set has none, refuting the claim.

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Review the concept: Construction of the naturals

The natural numbers are a set \(\mathbb{N}\) built inside set theory as finite ordinals, where each natural is the set of all naturals smaller than it.

\[n^+ = n \cup \{n\}\]

More practice problems: construction of the naturals

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