The purpose of this note is to point out: the principle of nested intervals is important not only in the theory of real number 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。
From the definition of real number, 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。
But a great number of experiments showed that there was a great differences between the real angular momentum and the anticipated value in theory.
大量的实验也表明实测的核素的自旋角动量与理论预测值之间有相当大的差距。
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