区间套定理在证明中值定理中的应用

Application of theorem of nested interval in proving mean value theorems

对区间套定理给出一个推论,然后建立了四个引理.在此基础上通过构造区间套依次证明了罗尔中值定理、拉格朗日中值定理和柯西中值定理.

Theorem of nested interval is one of the completeness theorems of real number, it is important in real analysis. This paper gives a corollary of theorem of nested interval and four lemmas. On the basis of these theories, Rolle mean value theorem, Lagrange mean value theorem and Cauchy mean value theorem are proved by constructing nested interval.