[…] all the elaborate expoundings of these impudent empirics, who are a million times worse than the worst of Catholic Priests.
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The easy proof is obtained applying the pigeon-hole principle to 𝛼₁x_1+…+𝛼ₙx_n(mod 1)|x_i=0,…N, or by geometry of numbers by applying Minkowski's first theorem in C.2.19 to the symmetric convex body of volume 2ⁿ⁺¹ given by |X_0+𝛼₁X_1+…𝛼ₙX_n|<N⁻ⁿ,|X_i|<N,i=1,…N.
This observation is an important leg of my argument.
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