鸽巢原理

鸽巢原理,又名狄利克雷抽屉原理、鸽笼原理。
其中一种简单的表述法为:
- 若有n个笼子和n+1只鸽子,所有的鸽子都被关在鸽笼里,那么至少有一个笼子有至少2只鸽子。
另一种为:
- 若有n个笼子和kn+1只鸽子,所有的鸽子都被关在鸽笼里,那么至少有一个笼子有至少k+1只鸽子。
拉姆齐定理是此原理的推广。
单词 | Pigeonhole principle |
释义 |
Pigeonhole principle
中文百科
鸽巢原理![]() 鸽巢原理,又名狄利克雷抽屉原理、鸽笼原理。 其中一种简单的表述法为:
另一种为:
拉姆齐定理是此原理的推广。
英语百科
Pigeonhole principle 鸽巢原理![]() ![]() In mathematics, the pigeonhole principle states that if n items are put into m containers, with n > m, then at least one container must contain more than one item. This theorem is exemplified in real life by truisms like "there must be at least two left gloves or two right gloves in a group of three gloves". It is an example of a counting argument, and despite seeming intuitive it can be used to demonstrate possibly unexpected results; for example, that two people in London have the same number of hairs on their heads (see below). |
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