Assume that $a=1$ and $b=1$. Then we trivially have


Multiply both sides with $a$


Substract $b^2$ from each side


Rewrite by factorizing


Cancelling $(a-b)$ from both sides gives


Since $a=1$ and $b=1$ we get


Q.E.D. ?

3 thoughts on “1=2”

  1. When dividing by (a-b) you just divided by zero. At that point, all it lost.

  2. @Ansolem
    That was obvious of course. Nonetheless, these fallacies remain pretty interesting. I’ll post another one soon where I’ll ‘proof’ that 1 is equal to -1 where, just as in this proof, some basic rules can be overseen.

  3. The line after your sentence is false sine a-b=o. We simplify only when a-b\neq 0.


Leave a Reply

Your email address will not be published. Required fields are marked *