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

zi2lalZ

zi2lalZ

Answered question

2020-11-07

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

Answer & Explanation

smallq9

smallq9

Skilled2020-11-08Added 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.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?