Brilli's proof of 0 = 1

Logic Level 2

Brilli the smartest kid in a school, gives a proof to the Brilliant community stating that 0 = 1. At what step number does it become unequal?

Here is his proof:

Step 1: 20 = 20 -20 = -20

Step 2: 16 36 = 25 45 16 - 36 = 25 - 45

Step 3: 4 2 4 × 9 = 5 2 5 × 9 4^2 - 4 \times 9 = 5^2 - 5 \times 9

Step 4: 4 2 4 × 9 + 81 4 = 5 2 5 × 9 + 81 4 4^2 - 4 \times 9 + \frac{81}{4}= 5^2 - 5 \times 9 + \frac{81}{4} {Just added it}

Step 5: 4 2 2 × 4 × 9 2 + ( 9 2 ) 2 = 5 2 2 × 5 × 9 2 + ( 9 2 ) 2 4^2 - 2 \times 4 \times \frac{9}{2} + (\frac{9}{2})^2 = 5^2 - 2 \times 5\times \frac{9}{2} + (\frac{9}{2})^2

Step 6: ( 4 9 2 ) ( 4 9 2 ) = ( 5 9 2 ) ( 5 9 2 ) (4 - \frac{9}{2})(4 - \frac{9}{2}) = (5 - \frac{9}{2})(5 - \frac{9}{2})

Step 7: ( 4 9 2 ) 2 = ( 5 9 2 ) 2 (4 - \frac{9}{2})^{2} = (5 - \frac{9}{2})^{2}

Step 8: 4 9 2 = 5 9 2 4 - \frac{9}{2} = 5 - \frac{9}{2}

Step 9: 4 = 5 4 = 5

Step 10: 0 = 1 \large \color{#20A900} \therefore 0 = 1

Step 4 Step 10 Step 7 Step 2 Step 8 Step 5 Step 3 Step 6

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2 solutions

Joshua Lowrance
May 22, 2018

4 - 9 2 \frac{9}{2} = - 1 2 \frac{1}{2}

5 - 9 2 \frac{9}{2} = 1 2 \frac{1}{2}

While (- 1 2 \frac{1}{2} )^2 = ( 1 2 \frac{1}{2} )^2, - 1 2 \frac{1}{2} does not equal 1 2 \frac{1}{2}

Saksham Jain
Nov 16, 2017

When we take square root .we take absolute value or +-

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