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

Negative numbers and coordinate plane
asked 2021-02-19
Show that the greatest lower bound of a set of positive numbers cannot be negative.

Answers (1)

Let S be the positive number i.e.,
S can be infinitely many times.
We know that a lower bound of a set is a element 'V ' of that set.
\(\displaystyle{V}\le{x}\) for all x sets .
In set S we can see that.
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 \(\displaystyle{G}\ge{l}\)
greatest lower bound is greater than any other lower bound
Let G be the greatest lower bound of a set S.
0 is a lower bound
Hence, the greatest lower bound set of positive numbers cannot be negative.
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