1=2

[latexpage]

Assume that $a=1$ and $b=1$. Then we trivially have

    $a=b$

Multiply both sides with $a$

    $a^2=ab$

Substract $b^2$ from each side

    $a^2-b^2=ab-b^2$

Rewrite by factorizing

    $(a+b)(a-b)=b(a-b)$

Cancelling $(a-b)$ from both sides gives

    $a+b=b$

Since $a=1$ and $b=1$ we get

    $2=1$.

Q.E.D. ?