Let S be the positive number i.e.,

\(S = {x in R: x >= 0}\)

S can be infinitely many times.

\(S = {1,3,9,11},[2,6],[10,50]\)

We know that a lower bound of a set is a element 'V ' of that set.

\(V<=x\)</span> for all x sets .

In set S we can see that.

\(X>=0\)

\(AA x in S\)

0 is always lower bound of S.

G is called the greatest lower bound of a set if for all lower bound 'l' of a set \(G >= l\)

greatest lower bound is greater than any other lower bound

Let G be the greatest lower bound of a set S.

\(G>=0\)

0 is a lower bound

Hence, the greatest lower bound set of positive numbers cannot be negative.

\(S = {x in R: x >= 0}\)

S can be infinitely many times.

\(S = {1,3,9,11},[2,6],[10,50]\)

We know that a lower bound of a set is a element 'V ' of that set.

\(V<=x\)</span> for all x sets .

In set S we can see that.

\(X>=0\)

\(AA x in S\)

0 is always lower bound of S.

G is called the greatest lower bound of a set if for all lower bound 'l' of a set \(G >= l\)

greatest lower bound is greater than any other lower bound

Let G be the greatest lower bound of a set S.

\(G>=0\)

0 is a lower bound

Hence, the greatest lower bound set of positive numbers cannot be negative.