Supremum and infimum for ordered sets For each of flic follo

For each of flic following ordered sets, consider the subset A. Find sup(yl) (or state it does not exist), and find inf(.4) (or state that it does not exist). Short answers are fine; no explanation is needed. Let 1R have the usual ordering, and let A = {1/n : n elemenof N} Let R have the usual ordering, and let A = [1,3] Let N have the usual ordering, and let A = {n element of N ; n is prime}

Solution

( a ) Let A = { 1/n : n N } then Sup ( A ) = 1 and Inf ( A ) = 0

( b )  Let A = [ 1 , 3 ) then A = { x : 1 x < 3 } so that Sup ( A ) = 3 and Inf ( A ) = 1

( c ) Let A = { n : n   N } then Then A = { 2 , 3 , 5 , 7 , 11 , 13 , 17 ... } so that Sup ( A ) = infinity and Inf ( A ) = 2