Ask question

# 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
Negative numbers and coordinate plane asked 2021-03-09
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.

### Relevant Questions asked 2021-02-23
Show that the greatest lower bound of a set of positive numbers cannot be negative. asked 2020-12-21
Show that the greatest lower bound of a set of positive numbers cannot be negative. asked 2021-02-19
Show that the greatest lower bound of a set of positive numbers cannot be negative. asked 2020-11-07
Show that the least upper bound of a set of negative numbers cannot be positive. asked 2020-11-22
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 asked 2021-01-31
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 asked 2021-01-10
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 asked 2021-01-10
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 asked 2020-10-28
Prove that every automorphism of R*, the group of nonzero real numbers under multiplication, maps positive numbers to positive numbers and negative numbers to negative numbers asked 2021-04-11
The equation F=−vex(dm/dt) for the thrust on a rocket, can also be applied to an airplane propeller. In fact, there are two contributions to the thrust: one positive and one negative. The positive contribution comes from air pushed backward, away from the propeller (so dm/dt<0), at a speed vex relative to the propeller. The negative contribution comes from this same quantity of air flowing into the front of the propeller (so dm/dt>0) at speed v, equal to the speed of the airplane through the air.
For a Cessna 182 (a single-engine airplane) flying at 130 km/h, 150 kg of air flows through the propeller each second and the propeller develops a net thrust of 1300 N. Determine the speed increase (in km/h) that the propeller imparts to the air.
...