Title: Given Any Two Statements, One of Them Implies the Other
Abstract: The statement of the title may come as a surprise. The proof is almost trivial as it is a tautology, but the mathematical and pedagogical consequences are important. In this talk, we will briefly prove this result and then discuss how we use the word “implies” as mathematicians and mathematics educators. We finally present an easy change to how one might present the idea of implication to the undergraduate student that may alleviate a lot of the common confusion about it.