erdos_354.parts.ii

Let $\alpha,\beta\in \mathbb{R}_{>0}$ such that $\alpha/\beta$ is irrational. Is \[\{ \lfloor \alpha\rfloor,\lfloor \gamma\alpha\rfloor,\lfloor \gamma^2\alpha\rfloor,\ldots\}\cup \{ \lfloor \beta\rfloor,\lfloor \gamma\beta\rfloor,\lfloor \gamma^2\beta\rfloor,\ldots\}\] complete?

theorem erdos_354.parts.ii : answer(sorry) ↔ ∃ γ ∈ Set.Ioo (1 : ℝ) 2, ∀ᵉ (α > 0) (β > 0), Irrational (α / β) →
    IsAddCompleteNatSeq' (FloorMultiples.interleave α β 2)

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