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AravindG

  • 2 years ago

does a=b always imply 1/a=1/b?

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  1. AshleyyWhuddupp
    • 2 years ago
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    yes,

  2. blockcolder
    • 2 years ago
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    Except of course when a=b=0 but otherwise, yeah.

  3. AravindG
    • 2 years ago
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    @badreferences , @apoorvk , @dumbcow , @dpaInc

  4. AravindG
    • 2 years ago
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    hmm...

  5. blockcolder
    • 2 years ago
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    If a=b, and they're not zero, you can divide both sides by ab to get 1/a=1/b.

  6. AravindG
    • 2 years ago
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    @EarthCitizen , @Ishaan94 , @Mani_Jha

  7. AravindG
    • 2 years ago
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    oh!! thats the answer i was looking for!!@blockcolder

  8. AravindG
    • 2 years ago
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    @blockcolder

  9. AravindG
    • 2 years ago
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    this seems a simple qn ..bt i had this doubt from my small classes

  10. EarthCitizen
    • 2 years ago
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    a=b, so long as a \[ a \neq0\]

  11. badreferences
    • 2 years ago
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    It's been answered, but a more rigorous way of answering it would be:\[\left\{a=b\mid\forall \left(ab\neq0\right)\right\}\]

  12. badreferences
    • 2 years ago
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    Whoops, I mean:\[\left\{a=b\therefore\frac{1}{a}=\frac{1}{b}\mid\forall \left(ab\neq0\right)\right\}\]

  13. badreferences
    • 2 years ago
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    As either \(a,b\) can be \(0\), but not necessarily both, for the implication to be demonstrably false. A simpler way of showing this is by determining that the product must not be zero.

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