实数连续性九个定理等价的证明

The Proof on the Equivalence among Nine Theorems of the Continuance of Real Number

用闭循环回路的方式证明了实数连续性的闭区间套定理,确界定理,有限覆盖定理,聚点定理,致密性定理,柯西收敛准则,单调有界数列存在极限定理,戴狄金基本定理,界点定理的彼此等价性。

In the analytic way of closed circle, this paper demonstrates nine theorems of the continuance of real number as follows： the regular theorem of closed and fixed area, the theorem of demarcation, the theorem of limited cove, the theorem of convergence, the extremely hermetic theorem, the theorem of A.L.Cauchy＇s restraint, the theorem of existing one-way definite numeral list, the theorem of Dedekind and the theorem of demarcation point, and especially proofs the equivalence among them.