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blackbird02

  • one year ago

Help in proving this inequality using the concepts or theorems on the properties of real numbers

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  1. blackbird02
    • one year ago
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  2. blackbird02
    • one year ago
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    Prove that if a>0, b<0, then \[ab+\frac{ b }{ a }<0\]

  3. triciaal
    • one year ago
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    |dw:1442641989956:dw|

  4. blackbird02
    • one year ago
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    what does ve stand for?

  5. triciaal
    • one year ago
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    sorry, -ve = negative and +ve = positive

  6. blackbird02
    • one year ago
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    I'm sorry, but I still don't get it. What would be my starting equation in the proving?

  7. zzr0ck3r
    • one year ago
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    \(ab<0 \text{ and } \frac{a}{b}<0\) so \(ab+\frac{a}{b}<0\)

  8. blackbird02
    • one year ago
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    @zzr0ck3r How would I prove this using the concepts or theorems on the properties of real numbers?

  9. blackbird02
    • one year ago
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    @Hero any idea how to prove this?

  10. Hero
    • one year ago
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    Are you still here.

  11. blackbird02
    • one year ago
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    Yeah

  12. Hero
    • one year ago
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  13. blackbird02
    • one year ago
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    @Hero just a clarification, in the seventh row, what is the equation? is it ab<0 +b/a<0 Or b/a<0 should be on another line?

  14. Hero
    • one year ago
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    It's one line: Two inequalities being added together

  15. blackbird02
    • one year ago
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    Oh, okay. I get it now. Thank you so much!

  16. Hero
    • one year ago
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    It's written exactly as it Should be

  17. triciaal
    • one year ago
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    @hero can you explain the step where you have "flip sign"?

  18. Hero
    • one year ago
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    b is negative If you multiply both sides of a>0 by a negative number, you have to invert the inequality symbol

  19. blackbird02
    • one year ago
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    @Hero Thank you so much!

  20. triciaal
    • one year ago
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    sorry, well thanks but that's the only place we differ on why a negative times a positive is negative. multiplication is group addition and we have a constant times a negative entity so it is more negative.

  21. zzr0ck3r
    • one year ago
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    "multiplication is group addition" ?

  22. triciaal
    • one year ago
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    @zzr0ck3r yes example 3 * 2 = 2 + 2 + 2 etc

  23. triciaal
    • one year ago
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    maybe repeated addition is better

  24. zzr0ck3r
    • one year ago
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    addition is the operation on the reals as a group multiplication is the other operation on the reals as a ring

  25. zzr0ck3r
    • one year ago
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    how would you write out (1/2)*(1/3) in those terms?

  26. triciaal
    • one year ago
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    what?

  27. zzr0ck3r
    • one year ago
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    google groups and rings.

  28. zzr0ck3r
    • one year ago
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    we start with a group an one operation addition we extend this idea to another operation called multiplication, once we have two operations and a few more properties we have a ring. we then include multiplicative inverses to close it up, and we get a field. All I am saying, is that sentence made no sense. ...

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