Combinatorial mathematics and its application--the principle of tolerance and repulsion

The principle of tolerance is often present in set theory, probability theory and combinatorial mathematics, and it is the generalization of the following conclusion.

This is because, we subtract separately | a|, | When b|, put | Ab| lost two times, so it should be added again.

Its generalization form is the tolerance theorem.

Before giving proof, it is necessary for us to fully understand the connotation of this formula. We discuss the number of objects (elements) that do not satisfy M-Properties based on a series of discrete elements on the s set. We assume that the specific manifestation of a certain property is: A ribbon, which Venn all the elements that satisfy this property (essentially, the picture), and now we want to ask for the number of elements that are not circled by a particular m-stripe.

This theorem can be used to make equivalent changes by using De Morgan Law, which plays an important role in counting and inversion formulas.

Combinatorial mathematics and its application--the principle of tolerance and repulsion