I am having trouble understanding how there could be a least upper bound for an open interval. If I have (a,b) and i am looking for the least upper bound X which is the number that is less than or equal to the set of Y such that Y> all the numbers in the interval (a,b) when I think about it I can't understand why it would be b. If the interval was (1,2) I would first think the lowest upper bound would be just to the left of 2. So 1.9999999 which would be a number with infinite decimals . I don't understand why it would be 2 as my textbooks says.