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