1=0 Part I

Algebra Level 4

Here is my attempt to demonstrate that 1 = 0 1=0 .

1) 0 = 0 0=0

2) 0 = 1 1 0=1-1

3) n 0 = n ( 1 1 ) n\cdot 0=n(1-1) , n n is a big natural number.

4) 0 = ( 1 1 ) + ( 1 1 ) + . . . + ( 1 1 ) n times 0=\underset { n\text{ times} }{ \underbrace { (1-1)+(1-1)+...+(1-1) } }

5) 0 = 1 1 + 1 1 0=1-1+1-\cdots -1

6) 0 = 1 ( 1 1 + 1 1 + ) 0=1-(1-1+1-1+\cdots)

7) 0 = 1 ( ( 1 1 ) + ( 1 1 ) + + ( 1 1 ) ) 0=1-((1-1)+(1-1)+\cdots +(1-1))

8) 0 = 1 ( 0 + 0 + + 0 ) 0=1-(0+0+\cdots + 0)

9) 0 = 1 0=1

In which step is the first error committed?


The answer is 7.

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1 solution

Joshua Chin
Apr 17, 2016

From step 5 we observe that the last term is 1 -1 . However in step 7 if we expand out, we realise that the last term is now 1 1 , not 1 -1 . Hence first mistake in step 7

Moderator note:

Ah yes, this was tricky because it didn't specify the parity of the terms.

Same thinking! (+1)

Noel Lo - 2 years, 11 months ago

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