Ivan Shishkin, Rye (1878)

Problems/Set theoryExercise

00 est plus grand que 11 ?

by FiniteField·
26
Difficulty scaleÉchelle de difficulté

This score reflects both the level of the required concepts and the difficulty of the solution.Ce score tient compte à la fois du niveau des notions nécessaires et de la difficulté de la résolution.

  1. 1–10First steps / middle schoolPremiers pas / collège
  2. 11–25Beginner / high schoolDébutant / lycée
  3. 26–50Intermediate / undergraduateIntermédiaire / licence
  4. 51–70Advanced / graduateAvancé / master
  5. 71–90Expert / specializedExpert / spécialisé
  6. 91–100Research levelNiveau recherche
These levels are approximate guides.Ces niveaux sont des repères approximatifs.
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ReviewedReviewed by darktoaster
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Français
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Pour a,b∈Na,b\in\mathbb{N} on pose a≺ba\prec b si a∣ba\mid b (aa divise bb).

  1. Montrer que ≺\prec est une relation d’ordre. Est-elle totale ?
  2. Montrer que 0=max⁡≺(N)0=\max\limits_{\prec}(\mathbb{N}) et 1=min⁡≺(N)1=\min\limits_{\prec}(\mathbb{N}).
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