(A new question of the week) I had a long discussion recently about the Cartesian product of sets, answering questions like, “How is it Cartesian?” and “How is it a product?” I like discussions about the relationships between different concepts, and people who ask these little-but-big questions. We’ll be looking at about a quarter of …
The arrival of 2020 has brought to mind the various controversies at the start of the year 2000, also called Y2K. As a software engineer responsible for date-sensitive communications within large computer systems, I well recall being on call that Saturday, in case something went wrong. I also recall all the questions we got in …
We’ve looked at some specific ideas about fractions (their proper definition, their relationship to decimals, and how to divide them); it’s time to go through this topic from the beginning. Here we’ll look at how they are introduced to beginners, and how to keep them from hurting our brains!
To finish up this long series on the order of operations, I want to look at where the “rules” came from, which will also demonstrate why some aspects are not fully agreed upon, finishing up the discussion from last time.
(An archive question of the week) Last time, as part of our series on estimation, we looked at some numerical methods for solving equations approximately. I mentioned the Method of False Position, but when I looked for more detailed expositions in our archive, I realized that in a sense it is really two different things, …