Answer
See below.
Work Step by Step
Answer may vary.
To proof by contradiction, we only need assume one and should not use the word $every$. Thus we can change the original proof as
"Suppose not. Suppose there exists an
integer $n$ which is irrational. Then we have
$n = n/1$, which is rational. This is a contradiction. [Hence
the supposition is false and the theorem is true.] ”