# 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.

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.

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|x − b| = -a
no solution
two negative solutions
two positive solutions
one positive and one negative solution
Let a and b be positive numbers such that a < b. State whether the absolute value equation has no solution, two negative solutions, two positive solutions, or one positive and one negative solution.
|x − b| = -a
no solution
two negative solutions
two positive solutions
one positive and one negative solution