Choose 13 real numbers $ x_1,x_2,\\ldots,x_{13}\\in\\mathbbb{R}<math/> with LaTeX Code: x_i\\neq x_j if LaTeX Code: i\\neq j . For these 13 numbers there exist at least two numbers amongst them such that LaTeX Code: 0 \\; < \\; \\frac{x_i-x_j}{1+x_ix_j} \\; \\leq \\; 2-\\sqrt{3} $
