Does two actually equal one?

Why is this called 2=1, one might ask. Here’s “proof” for something that’s wrong. If you’re able to appreciate these things, try finding the mistake.

a  =  b

a²  =  a b

a² + a²  =  a² + a b

2 a²  =  a² + a b

2 a² – 2 a b  =  a² + a b – 2 a b

2 a² – 2 a b  =  a² – a b

2 ( a² – a b )  =  1 ( a² – a b )

2  =  1

This will be the first and only geeky post, I promise.

Symbols and conventions are both ubiquitous and necessary in our every day life.  They enable our culture, on the one hand. On the other hand, they limit our imagination and we need to challenge them sometimes. This is a conflict I find fascinating and would like to base this blog on.

 

 

 

 

 

 

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4 thoughts on “Does two actually equal one?

  1. I assume no one has replied to this yet..
    This is really interesting but I think I know where the problem is.
    You are dividing by 0 when moving from the 2nd last line to the last line. (a^2-ab)=0
    It is really interesting though how the basics of algebra can be abused.

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