I need help with this question,
Does any open interval in R have a maximum? Explain your answer.
Thomas
Indirect proof: Suppose the open interval, (a, b), does have a maximum, M. Since M is in (a, b), a< M< b. Let .
Prove:
1) N< b.
2) a< M< N
so N is in (a, b)
3) M< N, contradicting the hypothesis.
Do you understand the difference between a "maximum" and a "supremum" (least upper bound)? That is crucial here.