Month: April 2019

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 …

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 …

Frequently Questioned Answers: Trisecting an Angle

One of the best ways to get people eager to do something is to tell them it can’t be done. When people who are not well-versed in mathematics learn that it is impossible to trisect an angle with compass and straightedge, they sometimes seem to make it their life goal to “do the impossible”. The …

More on 0.999…

(An archive question of the week) In collecting questions and answers about 0.999… for the last post, there were two that were too long to include, but that dig more deeply into issues that some of the standard answers tend to gloss over. So here, I want to look at those two answers, both of …

Frequently Questioned Answers: 0.999… = 1

Having looked at two common questions in probability that are often challenged, let’s turn to the realm of numbers. Non-terminating decimals are inherently problematic, and one particular example causes difficulty for many, even after they fully accept the mathematics of it. Our FAQ page on this topic, at 0.9999… = 1, is very brief, and …

Frequently Questioned Answers: The Other Child

This is the second in a series on Frequently Questioned Answers – that is, answers we have given that are often challenged by readers, either just out of confusion, or in the form of attacks on our intelligence or honesty. Here, we look at the problem of finding the probability that, given knowledge about one …