Pure math 3 : 2 = 1!

Calculus Level 3

Identify the first invalid step in the following proof.

  1. \(|x| = \underbrace{1 + 1 + 1 + ..... + 1}_{|x| \, \text{ times}} \)
  2. \(|x| \times |x| = \underbrace{|x + x + x + ..... + x|}_{|x| \, \text{ times}} \)
  3. \(x^2 = \underbrace{|x + x + x + ..... + x|}_{|x| \, \text{ times}} \)
  4. \(\dfrac{d}{dx}(x^2) = \dfrac{d}{dx}(\underbrace{|x + x + x + ..... + x|}_{|x| \, \text{ times}}) \)
  5. \(2x = \underbrace{1 + 1 + ..... + 1}_{|x| \, \text{ times}} \)
  6. \(2x = x \)
  7. \(2 = 1 \)
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