SOLUTION: Which of the following statements is false? a.There is a greatest negative integer. b.Between any two rational numbers, there is another rational number. c.Between any two irr

Algebra ->  Real-numbers -> SOLUTION: Which of the following statements is false? a.There is a greatest negative integer. b.Between any two rational numbers, there is another rational number. c.Between any two irr      Log On


   

Question 334147: Which of the following statements is false?
a.There is a greatest negative integer.
b.Between any two rational numbers, there is another rational number.
c.Between any two irrational numbers, there is another irrational number.
d.There is a least non-negative rational number.
e.There is a greatest negative rational number
Found 2 solutions by solver91311, amalm06:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Statements d and e are false.


John

My calculator said it, I believe it, that settles it

Answer by amalm06(224) About Me  (Show Source):
You can put this solution on YOUR website!
a. This is true. The least positive integer is 1, therefore the greatest negative integer is -1

b-c) Both are true. Can be proved with techniques from real analysis.

d. This would imply that the set of positive rational numbers, Q+, is bounded below. Therefore false.

e.) This would imply that the least positive rational number has an additive inverse. But the least positive rational number does not exist, by d). Therefore false.