Suppose not. That is, suppose that there is a least positive real number x. [We must reduce (a) ] Consider the number x/2. Since x is a positive real number, x/2 is also (b) . In addition, we can deduce that x/2 < x by multiplying both sides of the inequality 1 < 2 by (c) and dividing (d) . Hence x/2 is a positive real number that is less than the least positive real number. This is a (e)