存在性问题是数学研究中常遇到问题,存在性问题也可看作特殊的计数问题,即对某个集合A,讨论|A|≥1还是|A|=0。一般地说,所谓“存在”指的是“至少有一个”。这里仅须指明“存在”,并不需要指出是哪一个,也不要确定什么办法把这个存在的物体找出来,更没有“唯一”的含义。抽屉原理虽然简单、浅显,却正是解决存在性问题的强有力工具。原理1 把n+k(k≥1)个物体以任意方式全部放入n个抽屉中,一定存在一个抽屉,它里面有两个或更 Existential problems are often encountered in mathematics research. Existential problems can also be regarded as special counting problems. That is, for a certain set A, it is discussed whether |A|≥1 or |A|=0. In general, the so-called “existence” refers to “at least one.” It is only necessary to indicate “existence” here, and it does not need to indicate which one, and it is not necessary to determine what means to find this existing object, and there is no “unique” meaning. Although the drawer principle is simple and superficial, it is a powerful tool for solving existential problems. Principle 1 put n + k (k ≥ 1) objects in n drawers in any way, there must be a drawer, it has two or more