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…