实数完备性六大基本定理的等价性证明

The proof of the equivalence relations in the six fundamental theorems of completeness real numbers

利用有限覆盖定理作为公理,按照A(有限覆盖定理)→B(聚点定理)→C(区间套定理)→D(单调有界定理)→E(柯西收敛准则)→F(确界原理)→A顺序来证明实数完备性六大基本定理之间的等价性,从而更加真实地体现实数完备性六大基本定理之间的相互依存关系。

Abstract： In this paper, regarding restricted coverage theorem as axiom, we will prove their equivalence by symbol A→B→C→D→E→F→A,thus more really reflect the interdependence relationship of six fundamental theorems.