ELI5:<p>Constructive math is a philosophy of math where you must <i>construct</i> a value to proof its existence. The Intermediate Value Theorem states that if f(a) < 0 and f(b) > 0, then there exists a number c in the interval (a, b) where f(c) = 0. For the IVT to be constructive, you must be able to find c. (Technically, the theorem is Bolzano's theorem, not the IVT.)<p>The question asks why the Intermediate Value Theorem isn't constructive. The question provides a "binary search" for c.<p>The answer states that the proof doesn't work because checking whether a real number is 0 is undecidable. A real number is represented by an infinite sequence, and you can't tell if the sequence converges to 0.