Intermediate value theorem: Difference between revisions

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The intermediate value theorem states the following:

Consider anthe closed interval <math>I = [a,b]</math> of real numbers <math>\R</math> and a continuous function <math>f \colon I \to \R</math>. Then

*''Version I.'' if <math>u</math> is a number between <math>f(a)</math> and <math>f(b)</math>, that is, <math display="block">\min(f(a),f(b))<u<\max(f(a),f(b)),</math> then there is a <math>c\in (a,b)</math> such that <math>f(c)=u</math>.