This student has attempted to use proof by contradiction to show that there is no least positive rational number:

a. Identify the error in the student’s proof. 

b. Prove by contradiction that there is no least positive rational number.

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Assumption: There is a least positive rational number. Let this least positive rational number be n. As n is rational, n = where a and b are integers. a-b b Since a and b are integers, This contradicts the statement that n is the least positive rational number. Therefore, there is no least positive rational number. a n-1= -1 = a-b is a rational number that is less than n.