# Show that the least upper bound of a set of negative numbers cannot be positive.

Show that the least upper bound of a set of negative numbers cannot be positive.
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smallq9
Let s be the set of negative number i.e.,
$S=\left\{x\in R:x\le 0\right\}$ {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.
$u\ge x$ for all x set
In set S:
$0\ge x$
$\mathrm{\forall }x\in S$
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.