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''Except, must thou not multiply by zero, for therein lies the path to seeming proof of many false things.''

''Neither shall thy divide by zero, except for sufficiently large values of zero. That way calculus lies.''

to GoldenRuleOfAlgebra, but I disagree. The power really lies in applying the same function on both sides.
One just has to watch out, what happens if the op is not bijective.

Multiplication by zero is just a special case. The same problem occurs if you square or take absolute values.

And division by zero is out of the game anyway, because that it is not defined at all (on the usual number spaces).

-- GunnarZarncke

As my grandfather liked to point out, many false things can be 'proven' by ''dividing'' by zero:
      A^2 - A^2 = A^2 - A^2
   (A+A) * (A-A)= A * (A-A)    <-- Usually people think this step is suspect, while the next actually is.
          A + A = A
             2A = A
              2 = 1
Then again, going the other way would use multiplication by zero, so perhaps it ''is'' true. I like the ''except for sufficiently large values of zero'' part of the second one, though. -- ATS

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