Extreme value theorem

Question

How can the extreme value theorem be true if f(x)=x fits the criteria - it would be continuous on a closed interval - but it has no maximum or minimum?

Answer 1

 The extreme value theorem states that if a real-valued function f is continuous on the closed interval [a,b], then f must attain a maximum and a minimum, each at least once.

Note that it refers to a continuous real-values function on a closed interval [a,b]. f(x) = x meets the criteria if we consider a closed interval. In this case, the max is f(x) = b and the min is f(x) = a.