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

zi2lalZ 2020-11-07 Answered
Show that the least upper bound of a set of negative numbers cannot be positive.
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smallq9
Answered 2020-11-08 Author has 106 answers
Let s be the set of negative number i.e.,
S={xR:x0} {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.
ux for all x set
In set S:
0x
xS
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.
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