Sequences and supremum and infimum

Question

Let X = { 1.6, 1.66 , 1.666 , 1.6666 , ........}

Find supremum and infimum of X

Answer 1

First note that this sequence is strictly increasing, thus the infimum (greatest lower bound) is equal to the minimum, which is the first term in the sequence.

The sequence is also bounded from above (by 1.7, for instance). For any increasing sequence bounded from above, the supremum (least upper bound) is equal to the limit of the sequence, which is 5/3 in this case.