
Why Isn't the Intermediate Value Theorem Constructive? - TheAsprngHacker
https://math.stackexchange.com/questions/2947450/constructive-intermediate-value-theorem-ivt
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TheAsprngHacker
ELI5:

Constructive math is a philosophy of math where you must _construct_ 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.)

The question asks why the Intermediate Value Theorem isn't constructive. The
question provides a "binary search" for c.

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.

