Supremum and infimum

Question

X1 = { x | x = 0 or x = (1/n) ; n € N(N - set of natural numbers)

Find the supremum and infimum(if they exists ) of set X1

Answer 1

It might help to list a few elements of X1 = {0, 1/1, 1/2, 1/3, 1/4, 1/5, ....}.

The supremum is the smallest number greater than or equal to every element in X1. In this case, the largest element of X1 is 1/1 = 1, so that is our supremum (as no element of the set will be larger).

Similarly, the infimum is the largest number less than or equal to every element in X1. The set X1 includes 0, and all of the 1/n terms are strictly larger than 0, so 0 must be the infimum.