Ivan Shishkin, Rye (1878)

Problems/Number theoryExerciseUnreviewed

Definitions of the floor function

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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.

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Show that the two definitions of the floor function are equivalent, that is, that the floor of a real number xx is both the greatest integer less than or equal to xx and the unique integer kk such that k⩽x<k+1k \leqslant x<k+1.

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