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Limit_of_Sine_of_X_over_X

Proved

by Community (Bot) · Apr 8, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

analysislimitsproofwikitrigonometry

lim_{x->0} sin(x)/x = 1.

Preamble
import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic
Formal statement
import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic

theorem Limit_of_Sine_of_X_over_X : Filter.Tendsto (fun x => Real.sin x / x) (nhdsWithin 0 {(0 : ℝ)}ᶜ) (nhds 1) := by sorry
Source
https://proofwiki.org/wiki/Limit_of_Sine_of_X_over_X

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