Let S be the positive number i.e.,

\(\displaystyle{S}={\left\lbrace{x}\in{R}:{x}\ge{0}\right\rbrace}\)

S can be infinitely many times.

\(\displaystyle{S}={\left\lbrace{1},{3},{9},{11}\right\rbrace},{\left[{2},{6}\right]},{\left[{10},{50}\right]}\)

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

\(\displaystyle{V}\le{x}\) for all x sets .

In set S we can see that.

\(\displaystyle{X}\ge{0}\)

\(\displaystyle\forall{x}\in{S}\)

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 \(\displaystyle{G}\ge{l}\)

greatest lower bound is greater than any other lower bound

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

\(\displaystyle{G}\ge{0}\)

0 is a lower bound

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

\(\displaystyle{S}={\left\lbrace{x}\in{R}:{x}\ge{0}\right\rbrace}\)

S can be infinitely many times.

\(\displaystyle{S}={\left\lbrace{1},{3},{9},{11}\right\rbrace},{\left[{2},{6}\right]},{\left[{10},{50}\right]}\)

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

\(\displaystyle{V}\le{x}\) for all x sets .

In set S we can see that.

\(\displaystyle{X}\ge{0}\)

\(\displaystyle\forall{x}\in{S}\)

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 \(\displaystyle{G}\ge{l}\)

greatest lower bound is greater than any other lower bound

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

\(\displaystyle{G}\ge{0}\)

0 is a lower bound

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