Difference between revisions of "Proof that 2=1"

Revision as of 19:40, 27 June 2019

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

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

7) $2a = a$ . Addition.

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

Wait, What?

The error is dividing by (a-b). (a-b) is 0, so this proof divides by 0. Dividing by 0 is illegal. Thus, this proof is false.

@@ Line 16: / Line 16: @@
 Wait, What?
+The error is dividing by (a-b). (a-b) is 0, so this proof divides by 0.
+Dividing by 0 is illegal. Thus, this proof is false.