“PROVE” 2 = 0. CAN YOU FIND THE MISTAKE?
I received an email I wanted to share with you. Wolfgang came up with a false proof that 2 = 0. No one in his class, not even his teacher, could figure out the mistake. Can you? I present the false proof and the mistake in a new video. “Prove” 2 = 0. Can You Find The Mistake? Here is the “proof” in text. 2 = 1 + 1 2 = 1 + √(1) 2 = 1 + √(-1 * -1) 2 = 1 + √(-1)√(-1) 2 = 1 + i ( i ) 2 = 1 + i 2 2 = 1 + (-1) 2 = 0 Or keep reading for a text explanation. . . . . M I N D . Y O U R . D E C I S I O N S . . . . False Proof 2 = 0 2 = 1 + 1 2 = 1 + √(1) 2 = 1 + √(-1 * -1) 2 = 1 + √(-1)√(-1) 2 = 1 + i ( i ) 2 = 1 + i 2 2 = 1 + (-1) 2 = 0 The mistake is between lines 3 and 4. √(-1 * -1) ≠ √(-1)√(-1) This is a misapplication of the product rule for square roots. The product rule is guaranteed to work only when both values are positive. If x , y ≥ 0, then √( x y ) = √( x )√( y ) When x = y = -1, the product rule may not apply, an...