The minimax theorem for zero-sum games is easily proved from the strong duality theorem of linear programming. For the converse direction, the standard proof by Dantzig (1951) is massively incomplete, as we argue in this article. We explain and combine classical theorems about solving linear equations with nonnegative variables to give a correct alternative proof.

翻译：从线性编程的强烈双重理论中可以很容易地证明零和游戏的迷你数学理论。 在相反的方向上,丹兹吉格(1951年)的标准证据非常不完整,正如我们在本篇文章中所争论的那样。我们解释并结合了解决线性方程的经典理论和非负变量,以给出正确的替代证据。