8 Real analysis- Show that inf S consisting of elements of type 1/n is 0 using Archimedean property.

Book RG BARTLEY: Any real number a satisfying 0 is less than a is less than epsilon for every epsilon positive implies a=0. Show that inf S consisting of elements of type 1/n is 0 using Archimedean property. If y is greater than zero, there exists a natural number n such that n-1 is less than or equal to y is less than or equal to n (proof discussion using Archimedean property and well ordering property)