Art of Problem Solving

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Proof <math>2=1</math>:
Proof <math>2=1</math>:


Let <math>a=b</math>


<center> <math>a^2=ab</math> </center>  
Suppose that <math>a=b</math>


<center> <math>a^2-b^2=ab-b^2</math></center>
<math>
 
\begin{eqnarray*}
<center> <math>(a-b)(a+b)=b(a-b)</math></center>
a&=&b\\
 
a^2&=&ab\\
<center> <math>a+b=b</math></center>
a^2-b^2&=&ab-b^2\\
 
(a+b)(a-b)&=&b(a-b)\\
<center> <math>b+b=b</math></center>
a+b&=&b\\
 
b+b&=&b\\
<center> <math>2b=b</math></center>
2b&=&b\\
 
2&=&1
<center> <math>2=1</math></center>
\end{eqnarray*}
</math>

Revision as of 22:39, 23 May 2009

Awesome math solver from Puerto Rico, soon to be International Math Olympiad.


Proof $2=1$:


Suppose that $a=b$

$\begin{eqnarray*} a&=&b\\ a^2&=&ab\\ a^2-b^2&=&ab-b^2\\ (a+b)(a-b)&=&b(a-b)\\ a+b&=&b\\ b+b&=&b\\ 2b&=&b\\ 2&=&1 \end{eqnarray*}$ (Error compiling LaTeX. Unknown error_msg)