Albuquerque Journal - Parade - - TV - By Mar­i­lyn vos Sa­vant

One of my high school math teach­ers said that math­e­mat­ics is not an ex­act sci­ence and used a set of equa­tions to il­lus­trate his point. The re­sult was that 1 = 2. I don’t re­mem­ber the equa­tions. Do you know any­thing like this?

—Rus­sell Broad­wa­ter, Akron, Ohio Here’s an ex­am­ple:

If A = B, and you mul­ti­ply each side by A, you get A2 = AB. If you then sub­tract B2 from both sides, you get A2 - B2 = AB - B2. Fac­tor­ing the sides makes the equa­tion (A + B) (A - B) = B (A - B). Then di­vid­ing each side by (A - B) leaves A + B = B. And know­ing that A = B, this means that B + B = B, or 2B = B, or 2 = 1.

Crazy, right? But see where you di­vided both sides by (A - B)? You can’t do that. Why? Be­cause A and B are equal, A mi­nus B equals zero, and you can’t di­vide by zero. It’s true that math­e­mat­ics is not an ex­act sci­ence, but sets of fun equa­tions like these don’t prove it.

What’s the dif­fer­ence be­tween “luck” and “co­in­ci­dence”?

—Ja­nis An­der­son, Pear­land, Texas “Luck” is a ran­dom oc­cur­rence that op­er­ates ei­ther for or against us. “Co­in­ci­dence” is a ran­dom oc­cur­rence that brings two or more re­lated in­ci­dents to­gether. For ex­am­ple, “co­in­ci­dence” is what hap­pens when your two boyfriends head for your house at the same time. “Luck” is what hap­pens when one of their cars won’t start. Send ques­tions to