Which of the following is a correct statement?

Let the rational number be of the form , where p Z, while the rational number be r. If r + is a rational then we have that,

r + = for some a Z and b Z {0}. This means that r = - = where aq – bp Z and this contradicts the facts that r is irrational. Hence, our assumption that r + is a rational is false. Hence, it is an irrational number.