The following question is located on Page 80 of Calculus with Analytic Geometry by George Simmons.
Assume for a moment that the rational numbers are the only numbers that exist. Under this assumption, show that the Intermediate Value Theorem is false by considering the function $y=f(x)=x^2 - 2$ on the inteval $[1,2]$.
The only way I have been able to interpret this is to solve $f(x)$ for some irrational value. As the number would not exist in this hypothetical, the IVT would fail. However, I feel like that's an oversimplification and I'm missing what this question is actually asking me.