Art of Problem Solving

Proof that 2=1: Difference between revisions

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1) <math>a = b</math>. Given.
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2) <math>a^2 = ab</math>. Multiply both sides by a.
 
3) <math>a^2-b^2 = ab-b^2</math>.  Subtract <math>b^2</math> from both sides.
 
4) <math>(a+b)(a-b) = b(a-b)</math>.  Factor both sides.
 
5) <math>(a+b) = b</math>. Divide both sides by <math>(a-b)</math>
 
6) <math>a+a = a</math>.  Substitute <math>a</math> for <math>b</math>.
 
7) <math>2a = a</math>.  Addition.
 
8) <math>2 = 1</math>.  Divide both sides by <math>a</math>.
 
Wait, What?

Revision as of 12:17, 10 July 2019

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