Tag Archives: formal

PIE: proof by algebra

Posted on August 7, 2019 by Brent

In my previous post I stated a very formal, general form of the Principle of Inclusion-Exclusion, or PIE.1 In this post I am going to outline one proof of PIE. I’m not going to give a completely formal proof, because … Continue reading →

Posted in combinatorics, induction, pattern, proof | Tagged , , , , , , | 2 Comments

Formal PIE

Posted on July 27, 2019 by Brent

I’ve been talking informally about the Principle of Inclusion-Exclusion but I realized it would be useful to state it more formally before proceeding to some proofs. The only problem is that a fully formal statement of PIE has a lot … Continue reading →

Posted in combinatorics, pattern | Tagged , , , , , | 5 Comments