Bolzano-Weierstrass theorem

例句：

1. 1. The Bolzano-Weierstrass theorem is a fundamental concept in the field of number theory.
   博尔扎诺-维塞尔斯特拉斯定理是数论领域的基本概念。
2. 2. The Weierstrass theorem states that any continuous function can be approximated by a polynomial.
   维塞尔斯特拉斯定理表明，任何连续函数都可以用多项式来近似。
3. 3. In mathematics, the Bolzano-Weierstrass theorem is used to prove the existence of solutions for certain types of differential equations.
   在数学中，博尔扎诺-维塞尔斯特拉斯定理被用来证明某些类型的微分方程的解的存在性。