Monthly Archives: March 2020

An exploration of forward differences for bored elementary school students

Posted on March 22, 2020 by Brent

Last week I made a mathematics worksheet for my 8-year-old son, whose school is closed due to the coronavirus pandemic. I’m republishing it here so others can use it for similar purposes. Figurate numbers and forward differences There are lots … Continue reading →

Posted in arithmetic, teaching | Tagged , , , , , | 1 Comment

Ways to prove a bijection

Posted on March 17, 2020 by Brent

You have a function and want to prove it is a bijection. What can you do? By the book A bijection is defined as a function which is both one-to-one and onto. So prove that is one-to-one, and prove that … Continue reading →

Posted in logic, proof | Tagged , , , , , , , , | 7 Comments

One-sided inverses, surjections, and injections

Posted on March 14, 2020 by Brent

Several commenters correctly answered the question from my previous post: if we have a function and such that for every , then is not necessarily invertible. Here are a few counterexamples: Commenter Buddha Buck came up with probably the simplest … Continue reading →

Posted in logic | Tagged , , , , , , | 1 Comment

Test your intuition: bijections

Posted on March 3, 2020 by Brent

Suppose we have sets and and a function (that is, ’s domain is and its codomain is ). Suppose there is another function such that for every . Is necessarily a bijection? That is, does necessarily match up each element … Continue reading →

Posted in logic | Tagged , , , | 12 Comments