Ivan Shishkin, Rye (1878)

Problems/TopologyExerciseUnreviewed

La distance discrète

by Ancient Tree·
23
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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Soit XX un ensemble non vide. Montrer que la fonction d ⁣:X×X→Rd\colon X\times X\to \R telle que :
∀x,y∈X,d(x,y)={1 si x≠y0 sinon \forall x,y\in X, d(x, y)= \begin{cases}1 & \text { si } x\neq y \\ 0 & \text { sinon }\end{cases}est une distance sur XX, appelée la distance discrète.

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