Editing Continuous function (section)

====Extreme value theorem====
The [[extreme value theorem]] states that if a function ''f'' is defined on a closed interval <math>[a, b]</math> (or any closed and bounded set) and is continuous there, then the function attains its maximum, i.e. there exists <math>c \in [a, b]</math> with <math>f(c) \geq f(x)</math> for all <math>x \in [a, b].</math> The same is true of the minimum of ''f''. These statements are not, in general, true if the function is defined on an open interval <math>(a, b)</math> (or any set that is not both closed and bounded), as, for example, the continuous function <math>f(x) = \frac{1}{x},</math> defined on the open interval (0,1), does not attain a maximum, being unbounded above.