Hilbert basis theorem

例句：

1. 1. The Hilbert basis theorem states that a vector space must have a basis consisting only of its own elements.
   希尔伯特基底定理指出，一个向量空间必须只包含其自身的元素作为基。
2. 2. In mathematics, the Hilbert basis theorem is used to prove the existence of vector spaces.
   在数学中，希尔伯特基底定理被用来证明向量空间的存在性。
3. 3. The Hilbert basis theorem has been applied in various fields such as physics and computer science.
   希尔伯特基底定理已被应用于物理学和计算机科学等领域。