Month: May 2025

Combinatorial Proofs: Counting the Same Thing in Two Different Ways

We’ll first look at several old questions about proving a relationship between permutations or combinations, where we’ll see some algebraic proofs using formulas, and others that center on the meaning of the symbols as ways of counting. The latter are called “combinatorial proofs”. We’ll end with a recent question of the same type, which suggested …

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Sign Issues in Integration

Several recent questions involve things that go wrong with signs in integrating, and reveal some subtleties that are easily overlooked. We’ll also see some creative thinking!