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.,

$S=\{x\in R:x\le 0\}$ {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.

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.

In set 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.

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