Posted by: **Dave Richeson** | December 18, 2008

## Fallacies, Flaws, and Flimflam it’s been good to know ya

At the end of 2008 the *College Mathematics Journal* will stop running its 20-year column “Fallacies, Flaws, and Flimflam.” The column was devoted to “mistakes, fallacies, howlers, anomalies, and the like”â€”usually found on student work. In honor of the departure of this entertaining column I submit the following FFF which was submitted as a solution to a homework problem in my Discrete Mathematics class.

Prove or disprove: the quotient of any two rational numbers is rational.

False. We will present a counterexample. The numbers 22 and 7 are rational. However and is irrational. Thus the conjecture is false.

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I can beat that with a submission from my geometry class. I forget what the theorem was the student was proving, but the first line was: “We will begin by assuming the conclusion.”

By:

Robert Talberton December 18, 2008at 10:54 am

Excellent! At least (s)he was being clear about her/his assumptions!

By:

Dave Richesonon December 18, 2008at 11:14 am

22/7 and pi are extremely close, but they are not equal.

By:

Stephenon February 22, 2012at 7:12 pm

Exactly. That’s what makes this funny. :-)

By:

Dave Richesonon February 22, 2012at 8:33 pm

However, perhaps the student was right —> 1/0 is not a rational number. So there is a counterexample that shows the statement is false.

By:

Stevenon January 30, 2013at 1:32 am

Exactly—it is false, and that was the counterexample I was looking for.

By:

Dave Richesonon January 30, 2013at 10:36 am