Let s be the set of negative number i.e.,

\(\displaystyle{S}={\left\lbrace{x}\in{R}:{x}\le{0}\right\rbrace}\) {x be any negative number}

The least upper bound of s cannot be positive.

We know that an upper bound of a set is an element 'say' u belongs to that set.

\(\displaystyle{u}\ge{x}\) for all x set

In set S:

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

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

0 is an upper bound of 's'

S is not a set of all real numbers it is a set which contain negative numbers only.

\(\displaystyle{S}={\left\lbrace{x}\in{R}:{x}\le{0}\right\rbrace}\) {x be any negative number}

The least upper bound of s cannot be positive.

We know that an upper bound of a set is an element 'say' u belongs to that set.

\(\displaystyle{u}\ge{x}\) for all x set

In set S:

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

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

0 is an upper bound of 's'

S is not a set of all real numbers it is a set which contain negative numbers only.