用Dedekind分划定理证明实数完备性的几个定理

Confirmation of theorems of the completeness of real numbers by the Dedekind theorem

主要阐述了Dedekind分划定理证明问题的思想和方法,并运用Dedekind分划基本定理证明了单调有界定理、柯西收敛准则、一致连续性定理以及洛尔中值定理等几个有关实数完备性的定理.

Given the using method of Dedekind theorem in confirmation, demonstrated how the Dedekind theorem is used to confirm the monotone and bounded theorem, tile Cauchy criterion for convergence theorem, the uniform continuity theorem, the differential mean value theorem and the other three theorems about the completeness of real numbers.