Editing Intermediate value theorem (section)

==In constructive mathematics==

In [[constructive mathematics]], the intermediate value theorem is not true. Instead, the weakened conclusion one must take states that the value may only be found in some range which may be arbitrarily small.

* Let <math>a</math> and <math>b</math> be real numbers and <math>f:[a,b] \to R</math> be a pointwise continuous function from the [[closed interval]] <math>[a,b]</math> to the real line, and suppose that <math>f(a) < 0</math> and <math>0 < f(b)</math>. Then for every positive number <math>\varepsilon > 0</math> there exists a point <math>x</math> in the unit interval such that <math>\vert f(x) \vert < \varepsilon</math>.<ref>{{cite journal|title=Interpolating Between Choices for the Approximate Intermediate Value Theorem | author=Matthew Frank|journal=Logical Methods in Computer Science|volume=16|issue=3|date=July 14, 2020| doi=10.23638/LMCS-16(3:5)2020|arxiv=1701.02227}}</ref>