Pure math 3 : 2 = 1!

Calculus Level 3

Identify the first invalid step in the following proof.

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

Viki Zeta by Viki Zeta , 19, India

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1 solution

Sabhrant Sachan
Jul 16, 2016

x 2 = x + x + x + ⋯ + x ⏟ x times is only true for x ∈ I + It is a discontinuous function , which means it is not differentiable x^2 = \underbrace{x+x+x+\cdots+x}_{x \text{times}} \text{ is only true for } x\in \mathbb I^{+} \\ \text{It is a discontinuous function , which means it is not differentiable }

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