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Possible Duplicate:
Finding the error in a proof

  1. $a=b$
  2. $ab=a^2$
  3. $ab-b^2=a^2-b^2$
  4. $b(a-b)=(a+b)(a-b)$
  5. $b= a+b$

Reminder the first step where $b = 2b$ So,

$1=2$

In this case in my opinion the wrong step is that in the third, because you can´t subtract $b^2$ from both sides.

This question it was taken from a math exam.

  • 0
    I wonder why the most common questions can't be researched on [a search engine] before being asked.2012-10-21

3 Answers 3

4

$a=b \implies a-b=0$

from step 4 to 5 you are dividing through by $a-b=0$.

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    @ViniciusL.Beserr$a$ a friend has asked me this before.2012-10-21
3

You divided by $a-b$ in step 5), which is zero by assumption 1).

3

The transition from step 4 to step 5 is wrong.$\rm a = b\qquad\Rightarrow \qquad a - b = 0$If $\rm \,a - b = 0\, $, then $\rm (a + b)(a - b) = b(a - b) $ can be written as $\rm 0(a + b) = 0b$

While what we do in the transition is, we divide both sides by $0$, hence breaking the so-called “fundamental rule”: never divide by zero!

  • 0
    Thanks for you commentary.2012-10-21