The following proofs are examples of fallacious proofs, namely that .
Then we have
(adding to both sides)
(factoring out a 2 on the LHS)
(dividing by )
The trick in this argument is when we divide by . Since , , and dividing by zero is illegal.
The first step never definitively ends at a certain number (it switches back and forth between 1 and 2). Thus, we can't equate it with itself while extending it infinitely.