“nonlocality confers tremendous potential on topological materials: If a property is not defined locally, then it cannot be destabilized by local defects… The topological age thus promises a class of materials with unusually robust properties.” https://t.co/Ydg8S0XgoG
Proof. If π=a/b with a,b∈ℕ then for any n∈ℕ the integral aⁿπⁿ⁺¹ ∫₀¹ sin(πx) {xⁿ(1–x)ⁿ/n!} dx is an integer (apply integration by parts 2n-times & use a/π=b). But 0 < aⁿπⁿ⁺¹ ∫₀¹ sin(πx) xⁿ(1–x)ⁿ/n! dx < aⁿπⁿ⁺¹/n! < 1 for n large enough. QED pic.twitter.com/MjD1if1cAz
Proof. If eᵐ=a/b with a,b∈ℕ then for any n∈ℕ the integral b ∫₀¹ {eᵐˣm²ⁿ⁺¹} {xⁿ(1–x)ⁿ/n!} dx is an integer (use beᵐ=a & integration by parts 2n-times) But 0 < b ∫₀¹ eᵐˣm²ⁿ⁺¹xⁿ(1–x)ⁿ/n! dx < beᵐm²ⁿ⁺¹/n! < 1 for n large enough. QED pic.twitter.com/nIorpUtxhX
