Show that the greatest lower bound of a set of positive numbers cannot be negative.

Show that the greatest lower bound of a set of positive numbers cannot be negative.

Question
Show that the greatest lower bound of a set of positive numbers cannot be negative.

Answers (1)

2021-03-10
Let S be the positive number i.e.,
\(S = {x in R: x >= 0}\)
S can be infinitely many times.
\(S = {1,3,9,11},[2,6],[10,50]\)
We know that a lower bound of a set is a element 'V ' of that set.
\(V<=x\)</span> for all x sets .
In set S we can see that.
\(X>=0\)
\(AA x in S\)
0 is always lower bound of S.
G is called the greatest lower bound of a set if for all lower bound 'l' of a set \(G >= l\)
greatest lower bound is greater than any other lower bound
Let G be the greatest lower bound of a set S.
\(G>=0\)
0 is a lower bound
Hence, the greatest lower bound set of positive numbers cannot be negative.
0

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