Question

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

Answer 1

yes,

Answer 2

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

Answer 3

@badreferences , @apoorvk , @dumbcow , @dpaInc

Answer 4

hmm...

Answer 5

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

Answer 6

@EarthCitizen , @Ishaan94 , @Mani_Jha

Answer 7

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

Answer 8

@blockcolder

Answer 9

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

Answer 10

a=b, so long as a \[ a \neq0\]

Answer 11

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

Answer 12

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

Answer 13

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.