My Favorite One-Liners: Part 44

In this series, I’m compiling some of the quips and one-liners that I’ll use with my students to hopefully make my lessons more memorable for them.

Today’s quip is something that I’ll use to emphasize that the meaning of the word “or” is a little different in mathematics than in ordinary speech. For example, in mathematics, we could solve a quadratic equation for $x$:

$x^2 + 2x - 8 = 0$

$(x+4)(x-2) = 0$

$x + 4 = 0 \qquad \hbox{OR} \qquad x - 2 = 0$

$x = -4 \qquad \hbox{OR} \qquad x = 2$

In this example, the word “or” means “one or the other or maybe both.” It could be that both statements are true, as in the next example:

$x^2 + 2x +1 = 0$

$(x+1)(x+1) = 0$

$x + 1 = 0 \qquad \hbox{OR} \qquad x + 1= 0$

$x = -1 \qquad \hbox{OR} \qquad x = -1$

However, in plain speech, the word “or” typically means “one or the other, but not both.” Here the quip I’ll use to illustrate this:

At the end of “The Bachelor,” the guy has to choose one girl or the other. He can’t choose both.