Proof that 2=1

Revision as of 00:57, 3 February 2020 by Shurong.ge (talk | contribs) (Error)

Proof

1) $a = b$. Given.

2) $a^2 = ab$. Multiply both sides by a.

3) $a^2-b^2 = ab-b^2$. Subtract $b^2$ from both sides.

4) $(a+b)(a-b) = b(a-b)$. Factor both sides.

5) $(a+b) = b$. Divide both sides by $(a-b)$

6) $a+a = a$. Substitute $a$ for $b$.

7) $2a = a$. Addition.

8) $2 = 1$. Divide both sides by $a$.

Error

The quantity of $a-b$ is $0$ as $a = b$, since one cannot divide by zero, the proof is incorrect from that point on.

Usually, if a proof proves a statement that is clearly false, the proof has probably divided by zero in some way.

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