实数完备性基本定理的相互证明（30个）
一.确界原理
1.确界原理
证明单调有界定理
证 不妨设
<Object: word/embeddings/oleObject1.bin>
为有上界的单调递增数列.
由确界原理，数列
<Object: word/embeddings/oleObject2.bin>
有上确界，令
<Object: word/embeddings/oleObject3.bin>
，下面证明：
<Object: word/embeddings/oleObject4.bin>
.对任意的
<Object: word/embeddings/oleObject5.bin>
，由上确界的定义，存在数列
<Object: word/embeddings/oleObject6.bin>
中某一项
<Object: word/embeddings/oleObject7.bin>
,使得：<Object: word/embeddings/oleObject8.bin>
.由于<Object: word/embeddings/oleObject9.bin>
单调递增,故对任意的
<Ob ...