Our goal is to finally settle the persistent problem in Diophantine Approximation of finding best inhomogeneous linear approximates. Classical results from the theory of continued fractions solve the special homogeneous case in the form of a complete sequence of normal approximates. Real expansions that allow the notion of normality to percolate into the inhomogeneous setting will provide us with the general solution.

翻译：我们的目标是最终解决在查明最佳异同线性线性近似物方面长期存在的问题。 持续分数理论的经典结果以正常近似数的完整序列形式解决了特殊单一情况。 允许正常性概念渗透到异异异环境的真正扩展将为我们提供总体解决方案。