关于有限集[n]及其子集若干性质的讨论

Discussion on the Nature of the Finite Set [n] and Its Subsets

有限集由于有有限多个子集,因而具有许多无限集合所不具有的性质;从n元有限集的所有k元子集元素和入手,得到了n元有限集的全体子集元素和Sn的计数公式,以及所有k阶子集的元素和Sn,k(k=0,1,2,…,n)的计数公式以及单峰性质和其他一些推论.

Because finite set contains limited subsets, it has many properties infinite set doesn＇ t have. This paper begins with the sum of all elements of subsets with k elements in finite set with n elements, gains calculating formula for Sn, the sum of all elements of subsets in finite set with n elements, and gets calculating formula for Sn.k （k = 0,1,2,…, n） , the sum of all elements of subsets with k order as well as unimodal nature and some other inferences.