tendsto_ceil_right — Mathlib

English

As x approaches from the left, fract tends to 1 with x approaching an integer from below, in the fract-topology sense.

Русский

При подходе слева fract стремится к 1, когда x приближается к целому снизу.

LaTeX

$$$$\lim_{y \to x^-} \operatorname{fract}(y) = 1.$$$$

Lean4

theorem tendsto_ceil_right (n : ℤ) : Tendsto (fun x => ceil x : α → α) (𝓝[>] n) (𝓝[≥] (n + 1)) :=
  ((tendsto_pure_pure _ _).comp (tendsto_ceil_right_pure_add_one n)).mono_right <| by rw [← @cast_one α, ← cast_add];
    exact pure_le_nhdsWithin le_rfl

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