Fallacious proof/2equals1
The following proofs are examples of fallacious proofs, namely that .
Contents
[hide]Proof 1
Let .
Then we have
(since )
(adding to both sides)
(factoring out a 2 on the LHS)
(dividing by )
Explanation
The trick in this argument is when we divide by . Since , , and dividing by zero is undefined.
Proof 2
Explanation
The given series does not converge. Therefore, manipulations such as grouping terms before adding are invalid.