Ivan Shishkin, Rye (1878)

Problems/Other

Récurrence sur le continu

by Dattier·
50
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 Ancient Tree
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Schéma de récurrence sur [−1,1][-1, 1] :

Soit PP une propriété sur [−1,1][-1, 1].

  1. Base : ∃a<b∈[−1,1],∀x∈]a,b[,  P(x)\exists a < b \in [-1,1], \quad \forall x \in ]a, b[, \; P(x)
  2. Hérédité : ∀x∈[−1,1],P(x)  ⟹  P(2x2−1)\forall x \in [-1, 1], \quad P(x) \implies P(2x^2 - 1)

A-t-on , alors ∀x∈[−1,1],P(x)?\forall x \in [-1, 1], \quad P(x)?

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Original problem

  1. les dattes à Dattier
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