Max, min, least upper, and greatest lower bound for sets question
The maximum of a set is the largest value in the set; however in this case you can show that there is no maximum. Given any value in the set, you can always find a larger value that is also in the set.
The least upper bound is the smallest number that is larger than every number in the set; to show that 'x' is the least upper bound of a set, you thus have to show two things:
1) show that x is larger than every element of the set (in other words, show that x is an upper bound for the set)
2) show that if y < x, then there must be some element of the set which is larger than y (show that no number smaller than x is also an upper bound)