Math is broken: 2 = 1

Algebra Level 2

Ok, I know there is a lot of 2 = 1 2=1 proof on the internet. And, as you can guess, I "invented" mine, so, the only thing you'll have is to enter the incorrect step (indicate the result of the step, so if the incorrect step is between 1 and 2, put 2). Just wanted to say that the title is incorrect, and ​no, math is not broken 😂.

  1. 2 = 1 + 1 2 =1+1

  2. 2 = 1 + ( − 1 ) ∗ ( − 1 ) 2 = 1 + (-1) * (-1)

  3. 2 = 1 + ( e π i ) 2 2 = 1 + (e^{πi})^2

  4. 2 = ( e π i ) 2 + ( e π i ) 2 2 = (e^{πi})^2 +(e^{πi})^2

  5. 2 = ( e π i ) 4 2 = (e^{\pi i})^4

  6. 2 4 = e π i \sqrt[4]{2}=e^{πi}

  7. 2 4 = − 1 \sqrt[4]{2} = -1

  8. 2 = ( − 1 ) 4 2 = (-1)^4

  9. 2 = 1 2 = 1 😱


The answer is 5.

Arthur Guiot by Arthur Guiot , 19, USA

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1 solution

Guy Alves
Jun 9, 2017

It happens at step five where the left hand side is squared instead of multiplied by 2.

(Also the format is off: it should be e π i e^{πi} .)

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Thanks, I didn’t see the little mistake, I fixed it 😊

Arthur Guiot - 4 years ago

@Arthur Guiot Just pointing out a typo: In your 8th step it should be 2=(-1)^4 instead of 2 = -1^4.

Siva Budaraju - 4 years ago

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