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Theorems · Theorem · general topology

AddCircle.denseRange_zsmul_coe_iff

∀ {a p : ℝ}, (DenseRange fun x => x • ↑a) ↔ Irrational (a / p)

The multiples of a number a are dense on a circle of length p iff a / p is irrational.

Defined in
Mathlib.Topology.Instances.AddCircle.DenseSubgroup
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Foundations
Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound

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