Difference between revisions of "Proof that 2=1"

Revision as of 14:09, 27 January 2020

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 $a$ .

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+==Proof==
+) <math>a = b</math>. Given.
+) <math>a^2 = ab</math>. Multiply both sides by a.
+) <math>a^2-b^2 = ab-b^2</math>.  Subtract <math>b^2</math> from both sides.
+) <math>(a+b)(a-b) = b(a-b)</math>.  Factor both sides.
+) <math>(a+b) = b</math>. Divide both sides by <math>(a-b)</math>
+) <math>a+a = a</math>.  Substitute <math>a</math> for <math>b</math>.
+) <math>2a = a</math>.  Addition.
+) <math>2 = 1</math>.  Divide both sides by <math>a</math>.