$a=b$

$a^2=ab$

$a^2-b^2=ab-b^2$

$(a+b)(a-b)=b(a-b)$

$a+b=b$

$2a=a$

$2=1$

What's wrong with this proof?

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Division by $a-b$ is the division by zero, which is strictly not allowed as it is undefined