AravindG
does a=b always imply 1/a=1/b?
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AshleyyWhuddupp
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yes,
blockcolder
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Except of course when a=b=0 but otherwise, yeah.
AravindG
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@badreferences , @apoorvk , @dumbcow , @dpaInc
AravindG
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hmm...
blockcolder
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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.
AravindG
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@EarthCitizen , @Ishaan94 , @Mani_Jha
AravindG
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oh!! thats the answer i was looking for!!@blockcolder
AravindG
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@blockcolder
AravindG
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this seems a simple qn ..bt i had this doubt from my small classes
EarthCitizen
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a=b, so long as a \[ a \neq0\]
badreferences
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It's been answered, but a more rigorous way of answering it would be:\[\left\{a=b\mid\forall \left(ab\neq0\right)\right\}\]
badreferences
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Whoops, I mean:\[\left\{a=b\therefore\frac{1}{a}=\frac{1}{b}\mid\forall \left(ab\neq0\right)\right\}\]
badreferences
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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.