Problem #PRU-100257

Problem

Let $n$ be some positive number. It is obvious that $$2n-1<2n.$$ Take another positive number $a$, and multiply both sides of the inequality by $(-a)$ $$-2na+a<-2na.$$ Now, subtracting $(-2na)$ from both sides of the inequality we get $a<0$.

Thus, ALL POSITIVE NUMBERS ARE NEGATIVE!