SOLUTION: If 0 < a < b, show that 1/b < 1/a. Is the restriction that a is positive necessary?

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Question 829376: If 0 < a < b, show that 1/b < 1/a. Is the restriction that a is positive necessary?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
If 0 < a < b, show that 1/b < 1/a. Is the restriction that a is positive necessary?
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Consider: a < b
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Divide thru by ab to get:
1/b < 1/a
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The latter operation is true if a and b are positive
or if a and b are both negative.
Why?::
Ans: Because ab will, in either case, be positive.
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Cheers,
Stan H.