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## AravindG 4 years ago does a=b always imply 1/a=1/b?

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1. anonymous

yes,

2. blockcolder

Except of course when a=b=0 but otherwise, yeah.

3. AravindG

@badreferences , @apoorvk , @dumbcow , @dpaInc

4. AravindG

hmm...

5. blockcolder

If a=b, and they're not zero, you can divide both sides by ab to get 1/a=1/b.

6. AravindG

@EarthCitizen , @Ishaan94 , @Mani_Jha

7. AravindG

oh!! thats the answer i was looking for!!@blockcolder

8. AravindG

@blockcolder

9. AravindG

this seems a simple qn ..bt i had this doubt from my small classes

10. EarthCitizen

a=b, so long as a $a \neq0$

11. anonymous

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. anonymous

Whoops, I mean:$\left\{a=b\therefore\frac{1}{a}=\frac{1}{b}\mid\forall \left(ab\neq0\right)\right\}$

13. anonymous

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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