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Beginning mathematical proof

  • Thread starter Testify
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  • #1
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Homework Statement



I originally made this thread for something else, but I have another problem that I need help with.

Suppose a and b are nonzero real numbers. Prove that if a < 1/a < b < 1/b then a < -1.

Homework Equations



A hint was given for the problem: Assume a < 1/a < b < 1/b. Now prove that a < 0, and then use this fact to prove that a < -1.


Thanks
 
Last edited:

Answers and Replies

  • #2
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For b, you're missing the inequality in the triangle inequality.
 
  • #3
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new problem bump
 
  • #4
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It's not like threads go in the landfill and pollute kindergarten playgrounds after we're done with them. No need to recycle. Make a new thread when you have a new problem.

For this problem, first think about what it means when [tex]a<\frac1a[/tex]. What values could [tex]a[/tex] have? You should identify two possibilities (two open intervals where [tex]a[/tex] could be). The second part of the inequality will let you narrow it down to one.
 

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