Jordan DuBeau Two-Point Sets: Applying the Mathematical Sledgehammer

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Induction and recursion can be collectively thought of as the hammer in our mathematical toolkit. They are simple, versatile, and ultimately indispensable in constructing our proofs. In this talk, we will present transfinite induction and recursion, which allow us to use the same proof ideas on larger and more complicated sets. This powered-up version of the hammer is the sledgehammer of mathematics. Join us as we use the sledgehammer to prove the existence of a two-point set: a set of points in the plane that intersects every straight line exactly twice.