\problemdata     
{proofs-1}           
{proofs, false proofs}              
{}              
{S94, S01 PS-1} 		
{S01 Karger}        	

\begin{problem}Verify or falsify the following proof that if $a$ and $b$
are two equal real numbers, then $a=0$.\\
\emph{Suggested proof:}
\begin{eqnarray*}
a&=&b \\
a^2&=&ab \\
a^2-b^2&=&ab-b^2 \\
(a-b)(a+b)&=&(a-b)b \\
a+b&=&b \\
a&=&0 
\end{eqnarray*}

\solution{
The proof is incorrect: One cannot divide the two sides of the
equation by $a-b$ since $a=b$. }

\end{problem}


