Suppose that ##f## is continuous on ##[a,b]## and let ##M## be any number between ##f(a)## and ##f(b)##.(adsbygoogle = window.adsbygoogle || []).push({});

Then, there exists a number ##c## (at least one) such that:

##a < c < b## and ##f(c) = M##

Why did the author restrict ##c## to ##(a,b)## rather than ##[a,b]##? After all, ##c ∈ [a,b] ⇒ c ∈ (a,b)##.

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# Intermediate value theorem

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