# Monthly Archives: March 2020

## An exploration of forward differences for bored elementary school students

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 | | 1 Comment

## Ways to prove a bijection

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 | | 7 Comments

## One-sided inverses, surjections, and injections

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 | | 1 Comment