Difference between revisions of "Proof that 2=1"

(Proof)
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4) <math>(a+b)(a-b) = b(a-b)</math>.  Factor 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>
+
5) <math>(a+b) = b</math>. Add both sides by <math>(a-b)</math>
  
 
6) <math>a+a = a</math>.  Substitute <math>a</math> for <math>b</math>.
 
6) <math>a+a = a</math>.  Substitute <math>a</math> for <math>b</math>.

Revision as of 14:11, 27 January 2020

Proof

1) $a = b$. Given.

2) $a^2 = ab$. Multiply both sides by a.

3) $a^2-b^2 = ab-b^2$. Subtract $b^2$ from both sides.

4) $(a+b)(a-b) = b(a-b)$. Factor both sides.

5) $(a+b) = b$. Add both sides by $(a-b)$

6) $a+a = a$. Substitute $a$ for $b$.

7) $2a = a$. Addition.

8) $2 = 1$. Divide both sides by $a$.

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