One aspect of mathematics that students often struggle with, particularly in geometry (which traditionally has been where proof is introduced), is writing proofs. Why do we need to learn about proofs? Why are proofs needed in the first place? Here are a few answers we’ve given to these questions.
(An archive question of the week) While I was researching for the post on uncountable sets, I ran across a discussion that didn’t quite fit, but raises interesting questions about how countable and uncountable sets can fit together. How can the rational numbers be countable, but the irrational numbers, which are closely intertwined with them, …
(A new question of the week) A recent question from a student working beyond what he has learned led to an interesting discussion of alternative methods for solving a minimization problem, both with and without calculus.
(An archive question of the week) Recently we looked at the question of how likely a two-child family with a boy is to have another boy (or, to the contrary, to also have a girl). Searching for those questions turned up another one of interest involving the gender of a pair of siblings: How do …
One of the questions we looked at in our recent survey of percent change problems involved percentages over 100%, which often confuse students. How can anything be more than 100%? Let’s look at a couple questions about that issue.
We have looked at how to calculate, apply, and undo a percent increase or decrease. Here we will look at some special terms used in business for percent increases, which have been a source of many questions over the years.
Having discussed how to calculate the percent change between two numbers, and how to apply such a change to one number to get a new number, we need to look at what may be one of the most common types of questions we get: reversing a percent change (increase or decrease) to find the original …
A question we got in March asked about working with percent increases. As I replied to this rather common topic, referring to an archived answer, I was reminded that this would is a very common type of question, and would be a good topic to cover in the blog. So that will be the topic …
We could continue forever discussing questions whose answers are frequently questioned; but let’s finish by looking at infinity itself. The concept is impossible to fully grasp, because we are finite, and all of our experience is finite. Mathematicians have worked out ways to deal with infinity, though, and the results are often counter-intuitive. That means …
Frequently Questioned Answers: Uncountable Infinities Read More »
As a penultimate post in this series on problems that trigger a lot of doubt or opposition, we’ll look at one that is usually asked just as a “How do you do this?” question, but occasionally gets responses from people who argue for alternative interpretations. Our FAQ is at Three Houses, Three Utilities, which explains …