# Why

## Why, in Logic, Does “False” Imply Anything?

In a class on symbolic logic, students are taught the truth tables that define the “logical connectives” ∧ (and), ∨ (or), ¬ (not), and → (if  … then). Everything makes sense until they are told that if p is false, then is true whether or not q is true. How can we say that “If pigs fly, then 2 is …

## Extraneous Solutions: Causes and Cures

The other day a student I was helping face to face asked how she can know when to check for extraneous solutions of an equation. I gave her a quick version of my standard answer, and the light went on! Today I want to share these thoughts here, because they are  very important in several …

## Why Do People Treat dy/dx as a Fraction?

(New question of the week) Here is a recent question from Fida, another long-time “patient” of ours at Ask Dr. Math:

## Why Must the Number of Variables Equal the Number of Equations?

(New question of the week) Now that we are receiving questions at the new site, we will be periodically posting some of those questions and answers, in addition to going back to particularly interesting questions from the old archive. This question (which I have slightly edited) came to The Math Doctors earlier this month, from …

## Why We Care About “Why”

(Archive question of the week) One day back in November, as I entered the community college where I teach, a man came in behind me with his son, probably about 3 years old. It was the first snowy day of the year, and the father stood on the mat wiping his feet, while the little …

## WHY Do We Add or Multiply in Probability?

Last time, we discussed how you know whether to add or multiply (or something else) in compound probability problems (like finding the probability that you will flip heads and roll an even number). But as I’ve said before, it’s often easier to remember a formula if you know why it is what it is. I’ll …

## Why Can’t You Divide by Zero?

Last time, I talked about students’ difficulties carrying out divisions that involve a  zero, which  reminded me of another issue that sounds almost the same, but is quite different: division of a number by zero. Students often either forget the rule they were taught, or they don’t believe the rule, or they just wonder about …

## Dividing Right to Left, Adding Left to Right

I now want to start looking more deeply at some specific questions at various levels, starting with arithmetic, then algebra and geometry. Students learning arithmetic (and their parents) tend to think in terms of following some rote procedure, just because “that’s the way it’s done”. Modern educators try to focus more on deep understanding, so …

## A Sample of Ask Dr. Math, Part 2: Questions Outside of School

In the first post, I gave a small sampling of questions we’ve had from students, parents, and teachers, all related to school, and discussed how we like to deal with these. But we also get many questions with no direct relation to school. These may come from people who actually use math in their work …