The purpose of this note is to point out: the principle of nested intervals is important not only in the theoryofrealnumber but for various applied problems.
区间套原理不仅在实数理论中是重要的，而且对于许多应用问题也是重要的。
2
From the definition ofrealnumber, deduces each basic theory successively, thus proving the equivalence.
从实数定义出发，依次推出各基本定理，从而证明其等价性。
3
But a great numberof experiments showed that there was a great differences between the real angular momentum and the anticipated value in theory.