Minus Two Equals Two

This is a common mistake that many beginner students of proofs make.

Namely, the assumption of the statement that is to be proved. The actual

form of the proof that has taken place can be summarized as follows. Suppose

P is the proposition we are to prove. That is$,$ P $=2=2.$ Let Q $=4=4.$

Then, we have; assume P$.$ Derive Q$.$ Since P $$ Q and Q is true, therefore

P is also true. But of course, by now, we know that the truthfulness of the

proposition Q along with the truthfulness of the conditional proposition P $$

Q does not imply the truthfulness of the proposition P$.$ In fact, whenever P

is false, P $$ Q is true for every proposition Q$.$ Hence, the statement, not

surprisingly, is incorrect.